DSpace Community:
http://hdl.handle.net/2117/3178
Fri, 19 Sep 2014 09:52:22 GMT
20140919T09:52:22Z
webmaster.bupc@upc.edu
Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació
no

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, 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, 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.

Energy and carbon emissions aware services allocation with delay for Data Centers
http://hdl.handle.net/2117/22066
Title: Energy and carbon emissions aware services allocation with delay for Data Centers
Authors: Guillén, Bernat; Hesselbach Serra, Xavier; Muñoz López, Francisco Javier; Klingert, Sonja
Abstract: This paper presents a new approach to service
assignment in Data Centers (DC), relating it to a classical
combinatory problem called Bin Packing Problem and adding
the possibility of delay and collaboration with users and energy
providers. This possibility proves to reduce in much the energy
consumption of the DC as well as the CO2 emissions.
Fri, 14 Mar 2014 13:05:00 GMT
http://hdl.handle.net/2117/22066
20140314T13:05:00Z
Guillén, Bernat; Hesselbach Serra, Xavier; Muñoz López, Francisco Javier; Klingert, Sonja
no
Virtualization, Energy savings, Carbon emissions, Data Centers, Allocation
This paper presents a new approach to service
assignment in Data Centers (DC), relating it to a classical
combinatory problem called Bin Packing Problem and adding
the possibility of delay and collaboration with users and energy
providers. This possibility proves to reduce in much the energy
consumption of the DC as well as the CO2 emissions.

Connectivity: properties and structure
http://hdl.handle.net/2117/22004
Title: Connectivity: properties and structure
Authors: Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
Abstract: Connectivity is one of the central concepts of graph theory, from both a theoret ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice maxmin characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and faulttolerant interconnection or communication networks.
Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].
Wed, 12 Mar 2014 12:00:55 GMT
http://hdl.handle.net/2117/22004
20140312T12:00:55Z
Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
no
Graph Theory, Connectivity
Connectivity is one of the central concepts of graph theory, from both a theoret ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice maxmin characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and faulttolerant interconnection or communication networks.
Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].

Further topics in connectivity
http://hdl.handle.net/2117/22000
Title: Further topics in connectivity
Authors: Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
Abstract: Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edgeconnectivity. First, we describe results concerning maximal (vertex or edge) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the socalled “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.
Wed, 12 Mar 2014 11:17:54 GMT
http://hdl.handle.net/2117/22000
20140312T11:17:54Z
Balbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel
no
Graph Theory, Connectivity
Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edgeconnectivity. First, we describe results concerning maximal (vertex or edge) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the socalled “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.

From clutters to matroids
http://hdl.handle.net/2117/21963
Title: From clutters to matroids
Authors: Fàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco Javier
Abstract: This paper deals with the question of completing a monotone increasing family of subsets to obtain the dependent sets of a matroid. More precisely, we provide several natural ways of transforming the clutter of the inclusion minimal subsets of the family into the set of circuits of a matroid.
Mon, 10 Mar 2014 12:57:39 GMT
http://hdl.handle.net/2117/21963
20140310T12:57:39Z
Fàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco Javier
no
Clutter, antichain, matroid, matroidal completion.
This paper deals with the question of completing a monotone increasing family of subsets to obtain the dependent sets of a matroid. More precisely, we provide several natural ways of transforming the clutter of the inclusion minimal subsets of the family into the set of circuits of a matroid.

Locating domination in graphs and their complements
http://hdl.handle.net/2117/21284
Title: Locating domination in graphs and their complements
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set
S
of a graph
G
is called
locatingdominating
,
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
LD
codes
and the cardinality of an LDcode is the
locationdomination number
. An LDset of a
graph
G
is
global
if
S
is an LDset of both
G
and its complement,
G
. In this work, we give
some relations between the locatingdominating sets and locationdomination number in
a graph and its complement
Mon, 20 Jan 2014 12:49:27 GMT
http://hdl.handle.net/2117/21284
20140120T12:49:27Z
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
no
A dominating set
S
of a graph
G
is called
locatingdominating
,
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
LD
codes
and the cardinality of an LDcode is the
locationdomination number
. An LDset of a
graph
G
is
global
if
S
is an LDset of both
G
and its complement,
G
. In this work, we give
some relations between the locatingdominating sets and locationdomination number in
a graph and its complement