Articles de revista http://hdl.handle.net/2117/335502 2021-04-12T14:55:58Z Caterpillars are antimagic http://hdl.handle.net/2117/340688 Caterpillars are antimagic Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos; Tey Carrera, Joaquín An antimagic labeling of a 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 u is the sum of the labels assigned to the edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here, we prove that caterpillars are antimagic by means of an O(nlogn) algorithm. 2021-03-02T08:39:38Z Lozano Bojados, Antoni Mora Giné, Mercè Seara Ojea, Carlos Tey Carrera, Joaquín An antimagic labeling of a 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 u is the sum of the labels assigned to the edges incident to u. A graph is called antimagic when it has an antimagic labeling. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic and the conjecture remains open even for trees. Here, we prove that caterpillars are antimagic by means of an O(nlogn) algorithm. Reappraising the distribution of the number of edge crossings of graphs on a sphere http://hdl.handle.net/2117/340298 Reappraising the distribution of the number of edge crossings of graphs on a sphere Alemany Puig, Lluís; Mora Giné, Mercè; Ferrer Cancho, Ramon Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of crossings on complete graphs and complete bipartite graphs whose vertices are located uniformly at random on the surface of a sphere assuming that vertex placements are independent from each other. Here we revise his derivation of that variance in the light of recent theoretical developments on the variance of crossings and computer simulations. We show that Moon's formulae are inaccurate in predicting the true variance and provide exact formulae. This is the version of the article before peer review or editing, as submitted by an author to Journal of Statistical Mechanics: Theory and Experiment.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1742-5468/aba0ab/meta. 2021-02-22T14:55:22Z Alemany Puig, Lluís Mora Giné, Mercè Ferrer Cancho, Ramon Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of crossings on complete graphs and complete bipartite graphs whose vertices are located uniformly at random on the surface of a sphere assuming that vertex placements are independent from each other. Here we revise his derivation of that variance in the light of recent theoretical developments on the variance of crossings and computer simulations. We show that Moon's formulae are inaccurate in predicting the true variance and provide exact formulae. Neighbor-locating colorings in graphs http://hdl.handle.net/2117/335501 Neighbor-locating colorings in graphs Alcón, Liliana; Gutierrez, Marisa; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel A k-coloring of a graph G is a k-partition of into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices belonging to the same color , 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 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 with neighbor-locating chromatic number n or . 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. 2021-01-19T09:49:18Z Alcón, Liliana Gutierrez, Marisa Hernando Martín, María del Carmen Mora Giné, Mercè Pelayo Melero, Ignacio Manuel A k-coloring of a graph G is a k-partition of into independent sets, called colors. A k-coloring is called neighbor-locating if for every pair of vertices belonging to the same color , 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 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 with neighbor-locating chromatic number n or . 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.