1.3k citations · 2.5k across the 50 of their papers we have counts for
56 papers
From the strong differential to Italian domination in graphs
A. Cabrera Martinez, J. A. Rodriguez-Velazquez
Given a graph and a subset of vertices , the external neighbourhood of is defined as , where…
From (secure) w-domination in graphs to protection of lexicographic product graphs
Abel Cabrera Martinez, Alejandro Estrada Moreno, Juan Alberto Rodriguez-Velazquez
Let be a vector of nonnegative integers such that . Let be a graph and the open neighbourhood of . We say that a function…
A note on double domination in graphs
Abel Cabrera Martinez, Juan A. Rodriguez-Velazquez
Recently, Haynes, Hedetniemi and Henning published the book Topics in Domination in Graphs, which comprises 16 contributions that present advanced topics in graph domination, featu…
From Italian domination in lexicographic product graphs to w-domination in graphs
A. Cabrera Martinez, A. Estrada-Moreno, J. A. Rodriguez-Velazquez
In this paper, we show that the Italian domination number of every lexicographic product graph can be expressed in terms of five different domination parameters of .…
Double domination in lexicographic product graphs
A. Cabrera Martinez, S. Cabrera Garcia, J. A. Rodriguez-Velazquez
In a graph , a vertex dominates itself and its neighbours. A subset is said to be a double dominating set of if dominates every vertex of at least…
Protection of graphs with emphasis on Cartesian product graphs
Magdalena Valveny, Juan Alberto Rodriguez-Velazquez
In this paper we study the weak Roman domination number and the secure domination number of a graph. In particular, we obtain general bounds on these two parameters and, as a conse…