%0 Journal Article
%T Well ve-covered graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Boutrig, Razika
%A Chellali, Mustapha
%A Meddah, NacĂ©ra
%D 2023
%\ 09/10/2023
%V
%N
%P -
%! Well ve-covered graphs
%K vertex-edge domination
%K independent vertex-edge domination
%K well ve-covered graphs
%K trees
%R 10.22049/cco.2023.28186.1469
%X A vertex $u$ of a graph $G=(V,E)$ ve-dominates every edge incident to $u$ as well as every edge adjacent to these incident edges. A set $S\subseteq V$ is a vertex-edge dominating set (or a ved-set for short) if every edge of $E$ is ve-dominated by at least one vertex in $S$. A ved-set is independent if its vertices are pairwise non-adjacent. The independent ve-domination number $i_{ve}(G)$ is the minimum cardinality of an independent ved-set and the upper independent ve-domination number $\beta_{ve}(G)$ is the maximum cardinality of a minimal independent ved-set of $G$. In this paper, we are interesting in graphs $G$ such that $i_{ve}(G)=\beta_{ve}(G)$, which we call well ve-covered graphs. We show that recognizing well ve-covered graphs is co-NP-complete, and we present a constructive characterization of well ve-covered trees.
%U https://comb-opt.azaruniv.ac.ir/article_14622_6165a82d2ed9db6dfc8bf158a220335d.pdf