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arXiv · 2008.00236

Double domination in lexicographic product graphs

A. Cabrera Martinez·S. Cabrera Garcia·J. A. Rodriguez-Velazquez
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Abstract

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 twice. The minimum cardinality among all double dominating sets of $G$ is the double domination number. In this article, we obtain tight bounds and closed formulas for the double domination number of lexicographic product graphs $G\circ H$ in terms of invariants of the factor graphs $G$ and $H$.

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BibTeXRIS

A. Cabrera Martinez, S. Cabrera Garcia, J. A. Rodriguez-Velazquez. 2020-08-01. Double domination in lexicographic product graphs. https://doi.org/10.1016/j.dam.2020.03.045

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