Reports de recerca
http://hdl.handle.net/2117/3180
Thu, 03 Sep 2015 02:30:44 GMT2015-09-03T02:30:44ZOn global location-domination in bipartite graphs
http://hdl.handle.net/2117/28318
On global location-domination in bipartite graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
Wed, 10 Jun 2015 00:00:00 GMThttp://hdl.handle.net/2117/283182015-06-10T00:00:00ZApproximate results for rainbow labelings
http://hdl.handle.net/2117/27843
Approximate results for rainbow labelings
Lladó Sánchez, Ana M.
Article de recerca
Tue, 14 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2117/278432015-04-14T00:00:00ZOn star-forest ascending subgraph decomposition
http://hdl.handle.net/2117/27841
On star-forest ascending subgraph decomposition
Aroca Farrerons, José María; Lladó Sánchez, Ana M.
Tue, 14 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2117/278412015-04-14T00:00:00ZDecomposing almost complete graphs by random trees
http://hdl.handle.net/2117/27840
Decomposing almost complete graphs by random trees
Lladó Sánchez, Ana M.
Tue, 14 Apr 2015 00:00:00 GMThttp://hdl.handle.net/2117/278402015-04-14T00:00:00ZOn perfect and quasiperfect domination in graphs
http://hdl.handle.net/2117/27709
On perfect and quasiperfect domination in graphs
Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M Luz
Fri, 28 Nov 2014 00:00:00 GMThttp://hdl.handle.net/2117/277092014-11-28T00:00:00ZGlobal location-domination in graphs
http://hdl.handle.net/2117/27680
Global location-domination in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A dominating set S of a graph G is called
locating-dominating, LD-setfor 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 (G). An LD-set
S of a graph G is global if it is an LD-set of both G and its complement G. The
global location-domination number g(G) is the minimum cardinality of a global LD-set of
G. In this work,we give some relations between locating-dominating sets and the location-domination number in a graph and its complement
Domination, Global domination, Locating domination, Complement graph, Block-cactus, Trees
Tue, 03 Dec 2013 00:00:00 GMThttp://hdl.handle.net/2117/276802013-12-03T00:00:00ZJacobi matrices and boundary value problems in distance-regular graphs
http://hdl.handle.net/2117/14821
Jacobi matrices and boundary value problems in distance-regular graphs
Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia
In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs.
Wed, 25 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2117/148212012-01-25T00:00:00ZA differential approach for bounding the index of graphs under perturbations
http://hdl.handle.net/2117/12078
A differential approach for bounding the index of graphs under perturbations
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Tue, 01 Mar 2011 00:00:00 GMThttp://hdl.handle.net/2117/120782011-03-01T00:00:00ZEdge-distance-regular graphs
http://hdl.handle.net/2117/11794
Edge-distance-regular graphs
Cámara Vallejo, Marc; Dalfó Simó, Cristina; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Edge-distance-regularity is a concept recently introduced by the authors which is
similar to that of distance-regularity, but now the graph is seen from each of its edges
instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with
the same intersection numbers for any edge taken as a root. In this paper we study
this concept, give some of its properties, such as the regularity of Γ, and derive some
characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the
(standard) incidence matrix. Also, the analogue of the spectral excess theorem for
distance-regular graphs is proved, so giving a quasi-spectral characterization of edgedistance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.
Fri, 11 Mar 2011 00:00:00 GMThttp://hdl.handle.net/2117/117942011-03-11T00:00:00ZConnected graph searching
http://hdl.handle.net/2117/9116
Connected graph searching
Barrière Figueroa, Eulalia; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos Touloupas, Dimitrios
In graph searching game the opponents are a set of searchers and a fugitive in a graph.
The searchers try to capture the fugitive by applying some sequence moves that include
placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture
by moving along unguarded paths. The search number of a graph is the minimum number
of searchers required to guarantee the capture of the fugitive. In this paper, we initiate
the study of this game under the natural restriction of connectivity where we demand that
in each step of the search the locations of the graph that are clean (i.e. non-accessible to
the fugitive) remain connected. We give evidence that many of the standard mathematical
tools used so far in the classic graph searching fail under the connectivity requirement. We
also settle the question on “the price of connectivity” that is how many searchers more
are required for searching a graph when the connectivity demand is imposed. We make
estimations of the price of connectivity on general graphs and we provide tight bounds
for the case of trees. In particular for an n-vertex graph the ratio between the connected
searching number and the non-connected one is O(log n) while for trees this ratio is always
at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for
all graphs. Our combinatorial results imply a complete characterization of connected graph
searching on trees. It is based on a forbidden-graph characterization of the connected search
number. We prove that the connected search game is monotone for trees, i.e. restricting
search strategies to only those where the clean territories increase monotonically does not
require more searchers. A consequence of our results is that the connected search number can
be computed in polynomial time on trees, moreover, we show how to make this algorithm
distributed. Finally, we reveal connections of this parameter to other invariants on trees
such as the Horton-Stralher number.
Sun, 26 Sep 2010 00:00:00 GMThttp://hdl.handle.net/2117/91162010-09-26T00:00:00Z