Abel Cabrera Martínez

activity

20172021

most citedDouble domination in lexicographic product graphs

29 citations · 51 across the 8 of their papers we have counts for

collaborators

9 papers

math.CO2021

Roman domination in direct product graphs and rooted product graphs

Abel Cabrera Martinez, Iztok Peterin, Ismael G. Yero

Let $G$ be a graph with vertex set $V (G)$ . A function $f : V (G) \to {0, 1, 2}$ is a Roman dominating function on $G$ if every vertex $v \in V (G)$ for which $f (v) = 0$ is adjacent…

math.CO2021★ 5 cited

A note on the k-tuple domination number of graphs

Abel Cabrera Martinez

In a graph $G$ , a vertex dominates itself and its neighbours. A set $D \subseteq V (G)$ is said to be a $k$ -tuple dominating set of $G$ if $D$ dominates every vertex of $G$ at least…

math.CO2021

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…

math.CO2021★ 13 cited

Total Roman 2-domination in graphs

Suitberto Cabrera Garcia, Abel Cabrera Martinez, Frank A. Hernandez Mira +1

Given a graph $G = (V, E)$ , a function $f : V \to {0, 1, 2}$ is a total Roman ${2}$ -dominating function if: (1) every vertex $v \in V$ for which $f (v) = 0$ satisfies that $\sum_{u…

math.CO2020★ 3 cited

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 $G \circ H$ can be expressed in terms of five different domination parameters of $G$ .…

math.CO2020★ 29 cited

Double domination in lexicographic product graphs

A. Cabrera Martinez, S. Cabrera Garcia, J. A. Rodriguez-Velazquez

In a graph $G$ , a vertex dominates itself and its neighbours. A subset $S \subseteq V (G)$ is said to be a double dominating set of $G$ if $S$ dominates every vertex of $G$ at least…

math.CO2020

Dominating the direct product of two graphs through total Roman strategies

Abel Cabrera Martinez, Dorota Kuziak, Iztok Peterin +1

Given a graph $G$ without isolated vertices, a total Roman dominating function for $G$ is a function $f : V (G) \to {0, 1, 2}$ such that every vertex with label 0 is adjacent…

math.CO2020★ 1 cited

A note on total co-independent domination in trees

Abel Cabrera Martínez, Frank A. Hernández Mira, José M. Sigarreta Almira +1

A set $D$ of vertices of a graph $G$ is a total dominating set if every vertex of $G$ is adjacent to at least one vertex of $D$ . The total domination number of $G$ is the minimum c…

math.CO2017

On computational and combinatorial properties of the total co-independent domination number of graphs

Abel Cabrera Martinez, Frank A. Hernandez Mira, Jose M. Sigarreta Almira +1

A subset $D$ of vertices of a graph $G$ is a total dominating set if every vertex of $G$ is adjacent to at least one vertex of $D$ . The total dominating set $D$ is called a total c…