Reports de recerca
http://hdl.handle.net/2117/332050
2024-07-18T23:48:32ZTotal domination in plane triangulations
http://hdl.handle.net/2117/332049
Total domination in plane triangulations
Claverol Aguas, Mercè; Garcia Olaverri, Alfredo Martin; Hernández Peñalver, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel Altarriba, Francisco Javier
2020-11-12T13:55:50ZClaverol Aguas, MercèGarcia Olaverri, Alfredo MartinHernández Peñalver, GregorioHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèTejel Altarriba, Francisco JavierMetric dimension of maximal outerplanar graphs
http://hdl.handle.net/2117/133862
Metric dimension of maximal outerplanar graphs
Claverol Aguas, Mercè; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Hernández Peñalver, Gregorio; Garcia Olaverri, Alfredo Martin; Tejel, Javier
2019-06-03T12:39:15ZClaverol Aguas, MercèHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèHernández Peñalver, GregorioGarcia Olaverri, Alfredo MartinTejel, JavierTrees whose even-degree vertices induce a path are antimagic
http://hdl.handle.net/2117/133369
Trees whose even-degree vertices induce a path are antimagic
Lozano Boixadors, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín
An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9–14].
2019-05-23T07:33:59ZLozano Boixadors, AntoniMora Giné, MercèSeara Ojea, CarlosTey Carrera, JoaquínAn antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9–14].The neighbor-locating-chromatic number of pseudotrees
http://hdl.handle.net/2117/131569
The neighbor-locating-chromatic number of pseudotrees
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Gonzalez, Marisa; Alcón, Liliana
Ak-coloringof a graphGis a partition of the vertices ofGintokindependent sets,which are calledcolors. Ak-coloring isneighbor-locatingif any two vertices belongingto the same color can be distinguished from each other by the colors of their respectiveneighbors. Theneighbor-locating chromatic number¿NL(G) is the minimum cardinalityof a neighbor-locating coloring ofG.In this paper, we determine the neighbor-locating chromatic number of paths, cycles,fans and wheels. Moreover, a procedure to construct a neighbor-locating coloring ofminimum cardinality for these families of graphs is given. We also obtain tight upperbounds on the order of trees and unicyclic graphs in terms of the neighbor-locatingchromatic number. Further partial results for trees are also established.
2019-04-10T04:28:24ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelGonzalez, MarisaAlcón, LilianaAk-coloringof a graphGis a partition of the vertices ofGintokindependent sets,which are calledcolors. Ak-coloring isneighbor-locatingif any two vertices belongingto the same color can be distinguished from each other by the colors of their respectiveneighbors. Theneighbor-locating chromatic number¿NL(G) is the minimum cardinalityof a neighbor-locating coloring ofG.In this paper, we determine the neighbor-locating chromatic number of paths, cycles,fans and wheels. Moreover, a procedure to construct a neighbor-locating coloring ofminimum cardinality for these families of graphs is given. We also obtain tight upperbounds on the order of trees and unicyclic graphs in terms of the neighbor-locatingchromatic number. Further partial results for trees are also established.Neighbor-locating colorings in graphs
http://hdl.handle.net/2117/121239
Neighbor-locating colorings in graphs
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Alcón, Liliana; Gutierrez, Marisa
A k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S i , the set of colors of the neighborhood of u is different from the set of colors of the neighborhood of v . The neighbor-locating chromatic number ¿ NL ( G ) is the minimum cardinality of a neighbor-locating coloring of G . We establish some tight bounds for the neighbor-locating chromatic number of a graph, in terms of its order, maximum degree and independence number. We determine all connected graphs of order n = 5 with neighbor-locating chromatic number n or n - 1. We examine the neighbor-locating chromatic number for two graph operations: join and disjoint union, and also for two graph families: split graphs and Mycielski graphs
2018-09-18T09:56:26ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelAlcón, LilianaGutierrez, MarisaA k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S i , the set of colors of the neighborhood of u is different from the set of colors of the neighborhood of v . The neighbor-locating chromatic number ¿ NL ( G ) is the minimum cardinality of a neighbor-locating coloring of G . We establish some tight bounds for the neighbor-locating chromatic number of a graph, in terms of its order, maximum degree and independence number. We determine all connected graphs of order n = 5 with neighbor-locating chromatic number n or n - 1. We examine the neighbor-locating chromatic number for two graph operations: join and disjoint union, and also for two graph families: split graphs and Mycielski graphs