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http://hdl.handle.net/2117/3178
Sat, 19 Apr 2014 17:19:41 GMT2014-04-19T17:19:41Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoCorrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 1223-1231
http://hdl.handle.net/2117/22446
Title: Corrigendum to "Algebraic characterizations of regularity properties in bipartite graphs" Eur. J. Combin. 34 (2013) 1223-1231
Authors: Abiad, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Description: Corrigendum d'un article anteriorment publicatMon, 31 Mar 2014 10:03:52 GMThttp://hdl.handle.net/2117/224462014-03-31T10:03:52ZAbiad, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel ÀngelnoThe (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral diameter
http://hdl.handle.net/2117/22316
Title: The (Delta,D) and (Delta,N) problems in double-step digraphs with unilateral diameter
Authors: Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel
Abstract: We study the (D;D) and (D;N) problems for double-step 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 double-step 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 double-step
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 verticesThu, 20 Mar 2014 13:31:57 GMThttp://hdl.handle.net/2117/223162014-03-20T13:31:57ZDalfó Simó, Cristina; Fiol Mora, Miquel ÀngelnoWe study the (D;D) and (D;N) problems for double-step 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 double-step 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 double-step
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 verticesAlgebraic 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 distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular 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 distance-regularity 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 distance-regularity 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 GMThttp://hdl.handle.net/2117/223122014-03-20T12:40:12ZAbiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel ÀngelnoBipartite graph, regular graph, distance-regular graph, eigenvalues, predistance polynomialsRegular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular 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 distance-regularity 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 distance-regularity 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.Edge-distance-regular graphs are distance-regular
http://hdl.handle.net/2117/22307
Title: Edge-distance-regular graphs are distance-regular
Authors: Cámara Vallejo, Marc; Dalfó Simó, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, Hiroshi
Abstract: A graph is edge-distance-regular when it is distance-regular 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 edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-regular 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 GMThttp://hdl.handle.net/2117/223072014-03-20T10:40:00ZCámara Vallejo, Marc; Dalfó Simó, Cristina; Delorme, Charles; Fiol Mora, Miquel Àngel; Suzuki, HiroshinoA graph is edge-distance-regular when it is distance-regular 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 edge-distance-regular graph G is distance-regular and homogeneous. More precisely, G is edge-distance-regular if and only if it is bipartite distance-regular 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 edge-distance-regular when it is distance-regular 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 edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-regular 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 GMThttp://hdl.handle.net/2117/220662014-03-14T13:05:00ZGuillén, Bernat; Hesselbach Serra, Xavier; Muñoz López, Francisco Javier; Klingert, SonjanoVirtualization, Energy savings, Carbon emissions, Data Centers, AllocationThis 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 max-min 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 fault-tolerant 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 GMThttp://hdl.handle.net/2117/220042014-03-12T12:00:55ZBalbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel ÀngelnoGraph Theory, ConnectivityConnectivity 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 max-min 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 fault-tolerant 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 edge-connectivity. 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 so-called “conditional connectivity,” are considered.
For unexplained terminology concerning connectivity, see §4.1.Wed, 12 Mar 2014 11:17:54 GMThttp://hdl.handle.net/2117/220002014-03-12T11:17:54ZBalbuena Martínez, Maria Camino Teófila; Fàbrega Canudas, José; Fiol Mora, Miquel ÀngelnoGraph Theory, ConnectivityContinuing 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 edge-connectivity. 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 so-called “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 GMThttp://hdl.handle.net/2117/219632014-03-10T12:57:39ZFàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco JaviernoClutter, 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
locating-dominating
,
LD-set
for
short, if every vertex
v
not in
S
is uniquely determined by the set of neighbors of
v
belonging to
S
. Locating-dominating sets of minimum cardinality are called
LD
-codes
and the cardinality of an LD-code is the
location-domination number
. An LD-set of a
graph
G
is
global
if
S
is an LD-set of both
G
and its complement,
G
. In this work, we give
some relations between the locating-dominating sets and location-domination number in
a graph and its complementMon, 20 Jan 2014 12:49:27 GMThttp://hdl.handle.net/2117/212842014-01-20T12:49:27ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoA dominating set
S
of a graph
G
is called
locating-dominating
,
LD-set
for
short, if every vertex
v
not in
S
is uniquely determined by the set of neighbors of
v
belonging to
S
. Locating-dominating sets of minimum cardinality are called
LD
-codes
and the cardinality of an LD-code is the
location-domination number
. An LD-set of a
graph
G
is
global
if
S
is an LD-set of both
G
and its complement,
G
. In this work, we give
some relations between the locating-dominating sets and location-domination number in
a graph and its complementNordhaus-Gaddum bounds for locating domination
http://hdl.handle.net/2117/21023
Title: Nordhaus-Gaddum bounds for locating domination
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Abstract: A dominating set S of graph G is called metric-locating–dominating if it is also locating, that is, if every vertex v is uniquely determined by its vector of distances to the vertices in S. If moreover, every vertex v not in S is also uniquely determined by the set of neighbors of v belonging to S, then it is said to be locating–dominating. Locating, metric-locating–dominating and locating–dominating sets of minimum cardinality are called β-codes, η-codes and λ-codes, respectively. A Nordhaus–Gaddum bound is a tight lower or upper bound on the sum or product of a parameter of a graph G and its complement View the MathML source. In this paper, we present some Nordhaus–Gaddum bounds for the location number β, the metric-location–domination number η and the location–domination number λ. Moreover, in each case, the graph family attaining the corresponding bound is fully characterized.Tue, 17 Dec 2013 11:50:01 GMThttp://hdl.handle.net/2117/210232013-12-17T11:50:01ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio ManuelnoA dominating set S of graph G is called metric-locating–dominating if it is also locating, that is, if every vertex v is uniquely determined by its vector of distances to the vertices in S. If moreover, every vertex v not in S is also uniquely determined by the set of neighbors of v belonging to S, then it is said to be locating–dominating. Locating, metric-locating–dominating and locating–dominating sets of minimum cardinality are called β-codes, η-codes and λ-codes, respectively. A Nordhaus–Gaddum bound is a tight lower or upper bound on the sum or product of a parameter of a graph G and its complement View the MathML source. In this paper, we present some Nordhaus–Gaddum bounds for the location number β, the metric-location–domination number η and the location–domination number λ. Moreover, in each case, the graph family attaining the corresponding bound is fully characterized.Some structural, metric and convex properties of the boundary of a graph
http://hdl.handle.net/2117/20898
Title: Some structural, metric and convex properties of the boundary of a graph
Authors: Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Seara Ojea, Carlos
Abstract: Let
u;v
be two vertices of a connected graph
G
. The vertex
v
is
said to be a
boundary vertex
of
u
if no neighbor of
v
is further away
from
u
than
v
. The boundary of a graph is the set of all its boundary
vertices. In this work, we present a number of properties of the
boundary of a graph under diÆerent points of view: (1) a realization
theorem involving diÆerent types of boundary vertex sets: extreme
set, periphery, contour, and the whole boundary; (2) the contour is a
monophonic set; and (3) the cardinality of the boundary is an upper
bound for both the metric dimension and the determining number
of a graphTue, 03 Dec 2013 12:14:54 GMThttp://hdl.handle.net/2117/208982013-12-03T12:14:54ZHernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Seara Ojea, CarlosnoBoundary, Contour, Extreme set, Graph convexity, Metric
dimension.Let
u;v
be two vertices of a connected graph
G
. The vertex
v
is
said to be a
boundary vertex
of
u
if no neighbor of
v
is further away
from
u
than
v
. The boundary of a graph is the set of all its boundary
vertices. In this work, we present a number of properties of the
boundary of a graph under diÆerent points of view: (1) a realization
theorem involving diÆerent types of boundary vertex sets: extreme
set, periphery, contour, and the whole boundary; (2) the contour is a
monophonic set; and (3) the cardinality of the boundary is an upper
bound for both the metric dimension and the determining number
of a graphLocating-dominating codes: Bounds and extremal cardinalities
http://hdl.handle.net/2117/20810
Title: Locating-dominating codes: Bounds and extremal cardinalities
Authors: Cáceres, Jose; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Abstract: In this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses should determine a malfunctioning processor or an intruder. Here, we present our contributions on λ-codes and η-codes concerning bounds, extremal values and realization theorems.Wed, 27 Nov 2013 11:55:50 GMThttp://hdl.handle.net/2117/208102013-11-27T11:55:50ZCáceres, Jose; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. LuznoNetwork problems, Graph theory, Codes on graphs, Covering codes, Locating dominating codesIn this work, two types of codes such that they both dominate and locate the vertices of a graph are studied. Those codes might be sets of detectors in a network or processors controlling a system whose set of responses should determine a malfunctioning processor or an intruder. Here, we present our contributions on λ-codes and η-codes concerning bounds, extremal values and realization theorems.Matchings in random biregular bipartite graphs
http://hdl.handle.net/2117/20809
Title: Matchings in random biregular bipartite graphs
Authors: Perarnau Llobet, Guillem; Petridis, Georgios
Abstract: We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Wed, 27 Nov 2013 11:49:54 GMThttp://hdl.handle.net/2117/208092013-11-27T11:49:54ZPerarnau Llobet, Guillem; Petridis, GeorgiosnoRandom biregular bipartite graphs, Perfect matchings, Commutative graphsWe study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Reviewing some results on fair domination in graphs
http://hdl.handle.net/2117/20340
Title: Reviewing some results on fair domination in graphs
Authors: Hansberg Pastor, Adriana
Abstract: A fair dominating set in a graph G is a dominating set S such that all vertices not in S are dominated by the same number of vertices from S; that is, every two vertices outside S have the same number of neighbors in S. The fair domination number fd(G) of G is the minimum cardinality of a fair dominating set. In this work, we review the results stated in [Caro, Y., Hansberg, A., and Henning, M., Fair domination in graphs, Discrete Math. 312 (2012), no. 19, 2905–2914], where the concept of fair domination was introduced. Also, some bounds on the fair domination number are derived from results obtained in [Caro, Y., Hansberg, A., and Pepper, R., Regular independent sets in graphs, preprint].Wed, 09 Oct 2013 07:54:45 GMThttp://hdl.handle.net/2117/203402013-10-09T07:54:45ZHansberg Pastor, AdriananoA fair dominating set in a graph G is a dominating set S such that all vertices not in S are dominated by the same number of vertices from S; that is, every two vertices outside S have the same number of neighbors in S. The fair domination number fd(G) of G is the minimum cardinality of a fair dominating set. In this work, we review the results stated in [Caro, Y., Hansberg, A., and Henning, M., Fair domination in graphs, Discrete Math. 312 (2012), no. 19, 2905–2914], where the concept of fair domination was introduced. Also, some bounds on the fair domination number are derived from results obtained in [Caro, Y., Hansberg, A., and Pepper, R., Regular independent sets in graphs, preprint].The spectral excess theorem for distance-biregular graphs
http://hdl.handle.net/2117/20218
Title: The spectral excess theorem for distance-biregular graphs
Authors: Fiol Mora, Miquel Àngel
Abstract: The spectral excess theorem for distance-regular graphs states that a regular
(connected) graph is distance-regular if and only if its spectral-excess equals its
average excess. A bipartite graphFri, 27 Sep 2013 10:03:53 GMThttp://hdl.handle.net/2117/202182013-09-27T10:03:53ZFiol Mora, Miquel ÀngelnoThe spectral excess theorem, Distance-biregular graph, Local spectra, Predistance polynomials.The spectral excess theorem for distance-regular graphs states that a regular
(connected) graph is distance-regular if and only if its spectral-excess equals its
average excess. A bipartite graph