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http://hdl.handle.net/2117/3178
Mon, 24 Nov 2014 12:33:54 GMT
20141124T12:33:54Z
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no

The graph distance game and some graph operations
http://hdl.handle.net/2117/24796
Title: The graph distance game and some graph operations
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Abstract: In the graph distance game, two players alternate in constructing a max
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphs
Fri, 21 Nov 2014 12:24:49 GMT
http://hdl.handle.net/2117/24796
20141121T12:24:49Z
Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
no
Distance game, graph operations
In the graph distance game, two players alternate in constructing a max
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphs

On the local spectra of the subconstituents of a vertex set and completely pseudoregular codes
http://hdl.handle.net/2117/24667
Title: On the local spectra of the subconstituents of a vertex set and completely pseudoregular codes
Authors: Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Abstract: In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudoregular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. (C) 2013 Elsevier B.V. All rights reserved.
Tue, 11 Nov 2014 09:51:20 GMT
http://hdl.handle.net/2117/24667
20141111T09:51:20Z
Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
no
Pseudodistanceregularity, Local spectrum, Subconstituents, Predistance polynomials, Completely regular code, GRAPHS, POLYNOMIALS
In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudoregular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. (C) 2013 Elsevier B.V. All rights reserved.

LDgraphs and global locationdomination in bipartite graphs
http://hdl.handle.net/2117/24527
Title: LDgraphs and global locationdomination in bipartite graphs
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set S of a graph G is a locatingdominatingset, LDset for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S . Locatingdominating sets of minimum cardinality are called LDcodes and the cardinality of an LDcode is the locationdomination number, ¿(G)¿(G). An LDset S of a graph G is global if it is an LDset for both G and its complement, View the MathML sourceG¯. One of the main contributions of this work is the definition of the LDgraph, an edgelabeled graph associated to an LDset, that will be very helpful to deduce some properties of locationdomination in graphs. Concretely, we use LDgraphs to study the relation between the locationdomination number in a bipartite graph and its complement.
Fri, 31 Oct 2014 12:08:44 GMT
http://hdl.handle.net/2117/24527
20141031T12:08:44Z
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
no
domination, location, complement graph, bipartite graph
A dominating set S of a graph G is a locatingdominatingset, LDset for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S . Locatingdominating sets of minimum cardinality are called LDcodes and the cardinality of an LDcode is the locationdomination number, ¿(G)¿(G). An LDset S of a graph G is global if it is an LDset for both G and its complement, View the MathML sourceG¯. One of the main contributions of this work is the definition of the LDgraph, an edgelabeled graph associated to an LDset, that will be very helpful to deduce some properties of locationdomination in graphs. Concretely, we use LDgraphs to study the relation between the locationdomination number in a bipartite graph and its complement.

The graph distance game and some graph operations
http://hdl.handle.net/2117/24526
Title: The graph distance game and some graph operations
Authors: Cáceres, Jose; Puertas, M. Luz; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphs
Fri, 31 Oct 2014 12:00:32 GMT
http://hdl.handle.net/2117/24526
20141031T12:00:32Z
Cáceres, Jose; Puertas, M. Luz; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
no
Distance game, graph operations
In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphs

Quantum Google in a complex network
http://hdl.handle.net/2117/24220
Title: Quantum Google in a complex network
Authors: Paparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel Angel
Abstract: We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced powerlaw behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scalefree and random networks.
Thu, 02 Oct 2014 17:35:16 GMT
http://hdl.handle.net/2117/24220
20141002T17:35:16Z
Paparo, Giuseppe Davide; Muller, Markus; Comellas Padró, Francesc de Paula; Martin Delgado, Miguel Angel
no
Computer science, Information technology, Information theory and computation, Quantum information, Complex networks
We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced powerlaw behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scalefree and random networks.

On the representability of the biuniform matroid
http://hdl.handle.net/2117/24101
Title: On the representability of the biuniform matroid
Authors: Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
Abstract: Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
© 2013, Society for Industrial and Applied Mathematics
Thu, 18 Sep 2014 16:05:12 GMT
http://hdl.handle.net/2117/24101
20140918T16:05:12Z
Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
no
matroid theory, representable matroid, biuniform matroid, secret sharing
Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
© 2013, Society for Industrial and Applied Mathematics

The degreediameter problem in maximal bipartite planar graphs
http://hdl.handle.net/2117/24097
Title: The degreediameter problem in maximal bipartite planar graphs
Authors: Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
Abstract: The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 1 if is odd and n = 3 2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( 2)bD/2c,
and another one is C(  2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (  2)k if D = 2k, and 3(  3)k if D = 2k + 1, for and D sufficiently large in both cases.
Thu, 18 Sep 2014 10:55:22 GMT
http://hdl.handle.net/2117/24097
20140918T10:55:22Z
Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
no
Maximal planar bipartite graphs
The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 1 if is odd and n = 3 2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( 2)bD/2c,
and another one is C(  2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (  2)k if D = 2k, and 3(  3)k if D = 2k + 1, for and D sufficiently large in both cases.

A bound for the maximum weight of a linear code
http://hdl.handle.net/2117/24092
Title: A bound for the maximum weight of a linear code
Authors: Ball, Simeon Michael; Blokhuis, Aart
Abstract: It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m &le (nd)pe(p1), where e {0, 1,.., k2} is maximal with the property that (nde) 0 (mod pk1e). Thus, if C contains a codeword of weight n, then nd/(p1)+d+e. The results obtained for linear codes are translated into corresponding results for (n, t)arcs and tfold blocking sets of AG(k1, q). The bounds obtained in these spaces are better than the known bounds for these geometrical objects for many parameters
Wed, 17 Sep 2014 17:03:50 GMT
http://hdl.handle.net/2117/24092
20140917T17:03:50Z
Ball, Simeon Michael; Blokhuis, Aart
no
Mathematical techniques
It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m &le (nd)pe(p1), where e {0, 1,.., k2} is maximal with the property that (nde) 0 (mod pk1e). Thus, if C contains a codeword of weight n, then nd/(p1)+d+e. The results obtained for linear codes are translated into corresponding results for (n, t)arcs and tfold blocking sets of AG(k1, q). The bounds obtained in these spaces are better than the known bounds for these geometrical objects for many parameters

Simulation of cable dynamics for moored ocean platforms: modeling aids design of large, underwater power cable
http://hdl.handle.net/2117/23616
Title: Simulation of cable dynamics for moored ocean platforms: modeling aids design of large, underwater power cable
Authors: Prat Farran, Joana d'Arc; Zaragoza Monroig, M. Luisa; Río Fernandez, Joaquín del
Fri, 25 Jul 2014 10:56:15 GMT
http://hdl.handle.net/2117/23616
20140725T10:56:15Z
Prat Farran, Joana d'Arc; Zaragoza Monroig, M. Luisa; Río Fernandez, Joaquín del
no

Perfect edgemagic graphs
http://hdl.handle.net/2117/22939
Title: Perfect edgemagic graphs
Authors: López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
Abstract: The study of the possible valences for edgemagic labelings of graphs has motivated us to introduce the concept of perfect edgemagic graphs. Intuitively speaking, an edgemagic graph is perfect edgemagic if all possible theoretical valences occur. In particular, we prove that for each integer m > 0, that is the power of an odd prime, and for each natural number n, the crown product Cm circle dot (Kn) over bar is perfect edgemagic. Related results are also provided concerning other families of unicyclic graphs. Furthermore, several open questions that suggest interesting lines for future research are also proposed.
Fri, 09 May 2014 09:45:58 GMT
http://hdl.handle.net/2117/22939
20140509T09:45:58Z
López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
no
Edgemagic, Perfect edgemagic, Valence, Digraph products, Labelings
The study of the possible valences for edgemagic labelings of graphs has motivated us to introduce the concept of perfect edgemagic graphs. Intuitively speaking, an edgemagic graph is perfect edgemagic if all possible theoretical valences occur. In particular, we prove that for each integer m > 0, that is the power of an odd prime, and for each natural number n, the crown product Cm circle dot (Kn) over bar is perfect edgemagic. Related results are also provided concerning other families of unicyclic graphs. Furthermore, several open questions that suggest interesting lines for future research are also proposed.

The (Delta,D) and (Delta,N) problems in doublestep digraphs with unilateral distance
http://hdl.handle.net/2117/22938
Title: The (Delta,D) and (Delta,N) problems in doublestep digraphs with unilateral distance
Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Abstract: We study the (delta;D) and (delta;N) problems for doublestep digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, the latter obtained by changing the directions of all the arcs. The first problem consists of maximizing the number of vertices N of a digraph, given the
maximum degree and the unilateral diameter D , whereas the second one (somehow dual of the first) consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the first problem for every value of the unilateral diameter and the second one
for infinitely many values of the number of vertices. Moreover, we compute the mean unilateral distance of the digraphs in the families considered.
Fri, 09 May 2014 09:30:19 GMT
http://hdl.handle.net/2117/22938
20140509T09:30:19Z
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
no
Unilateral distance, Doublestep, Digraphs
We study the (delta;D) and (delta;N) problems for doublestep digraphs considering the unilateral distance, which is the minimum between the distance in the digraph and the distance in its converse digraph, the latter obtained by changing the directions of all the arcs. The first problem consists of maximizing the number of vertices N of a digraph, given the
maximum degree and the unilateral diameter D , whereas the second one (somehow dual of the first) consists of minimizing the unilateral diameter given the maximum degree and the number of vertices. We solve the first problem for every value of the unilateral diameter and the second one
for infinitely many values of the number of vertices. Moreover, we compute the mean unilateral distance of the digraphs in the families considered.

Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 12231231
http://hdl.handle.net/2117/22446
Title: Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 12231231
Authors: Abiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Description: Corrigendum d'un article anteriorment publicat
Mon, 31 Mar 2014 10:03:52 GMT
http://hdl.handle.net/2117/22446
20140331T10:03:52Z
Abiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
no

The (Delta,D) and (Delta,N) problems in doublestep digraphs with unilateral diameter
http://hdl.handle.net/2117/22316
Title: The (Delta,D) and (Delta,N) problems in doublestep digraphs with unilateral diameter
Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Abstract: We study the (D;D) and (D;N) problems for doublestep digraphs considering
the unilateral distance, which is the minimum between the distance in the digraph
and the distance in its converse digraph, obtained by changing the directions
of all the arcs.
The first problem consists of maximizing the number of vertices N of a digraph,
given the maximum degree D and the unilateral diameter D , whereas the
second one consists of minimizing the unilateral diameter given the maximum
degree and the number of vertices. We solve the first problem for every value
of the unilateral diameter and the second one for some infinitely many values of
the number of vertices.
Miller and Sirán [4] wrote a comprehensive survey about (D;D) and (D;N)
problems. In particular, for the doublestep graphs considering the standard
diameter, the first problem was solved by Fiol, Yebra, Alegre and Valero [3],
whereas Bermond, Iliades and Peyrat [2], and also Beivide, Herrada, Balcázar
and Arruabarrena [1] solved the (D;N) problem. In the case of the doublestep
digraphs, also with the standard diameter, Morillo, Fiol and Fàbrega [5] solved
the (D;D) problem and provided some infinite families of digraphs which solve
the (D;N) problem for their corresponding numbers of vertices
Thu, 20 Mar 2014 13:31:57 GMT
http://hdl.handle.net/2117/22316
20140320T13:31:57Z
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
no
We study the (D;D) and (D;N) problems for doublestep digraphs considering
the unilateral distance, which is the minimum between the distance in the digraph
and the distance in its converse digraph, obtained by changing the directions
of all the arcs.
The first problem consists of maximizing the number of vertices N of a digraph,
given the maximum degree D and the unilateral diameter D , whereas the
second one consists of minimizing the unilateral diameter given the maximum
degree and the number of vertices. We solve the first problem for every value
of the unilateral diameter and the second one for some infinitely many values of
the number of vertices.
Miller and Sirán [4] wrote a comprehensive survey about (D;D) and (D;N)
problems. In particular, for the doublestep graphs considering the standard
diameter, the first problem was solved by Fiol, Yebra, Alegre and Valero [3],
whereas Bermond, Iliades and Peyrat [2], and also Beivide, Herrada, Balcázar
and Arruabarrena [1] solved the (D;N) problem. In the case of the doublestep
digraphs, also with the standard diameter, Morillo, Fiol and Fàbrega [5] solved
the (D;D) problem and provided some infinite families of digraphs which solve
the (D;N) problem for their corresponding numbers of vertices

Algebraic Characterizations of Regularity Properties in Bipartite Graphs
http://hdl.handle.net/2117/22312
Title: Algebraic Characterizations of Regularity Properties in Bipartite Graphs
Authors: Abiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Abstract: Regular and distanceregular characterizations of general graphs are wellknown. In particular, the spectral excess theorem states that a connected graph GG is distanceregular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distanceregularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the Hoffman polynomial. Moreover, it is shown that the conditions for having distanceregularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.
Thu, 20 Mar 2014 12:40:12 GMT
http://hdl.handle.net/2117/22312
20140320T12:40:12Z
Abiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
no
Bipartite graph, regular graph, distanceregular graph, eigenvalues, predistance polynomials
Regular and distanceregular characterizations of general graphs are wellknown. In particular, the spectral excess theorem states that a connected graph GG is distanceregular if and only if its spectral excess (a number that can be computed from the spectrum) equals the average excess (the mean of the numbers of vertices at extremal distance from every vertex). The aim of this paper is to derive new characterizations of regularity and distanceregularity for the more restricted family of bipartite graphs. In this case, some characterizations of (bi)regular bipartite graphs are given in terms of the mean degrees in every partite set and the Hoffman polynomial. Moreover, it is shown that the conditions for having distanceregularity in such graphs can be relaxed when compared with general graphs. Finally, a new version of the spectral excess theorem for bipartite graphs is presented.

Edgedistanceregular graphs are distanceregular
http://hdl.handle.net/2117/22307
Title: Edgedistanceregular graphs are distanceregular
Authors: Cámara Vallejo, Marc; Dalfó Simó, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
Abstract: A graph is edgedistanceregular when it is distanceregular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edgedistanceregular graph Γ is distanceregular and homogeneous. More precisely, Γ is edgedistanceregular if and only if it is bipartite distanceregular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers.
Thu, 20 Mar 2014 10:40:00 GMT
http://hdl.handle.net/2117/22307
20140320T10:40:00Z
Cámara Vallejo, Marc; Dalfó Simó, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
no
A graph is edgedistanceregular when it is distanceregular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edgedistanceregular graph G is distanceregular and homogeneous. More precisely, G is edgedistanceregular if and only if it is bipartite distanceregular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers.
A graph is edgedistanceregular when it is distanceregular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edgedistanceregular graph Γ is distanceregular and homogeneous. More precisely, Γ is edgedistanceregular if and only if it is bipartite distanceregular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers.