@article {
author = {Boutrig, Razika and Chellali, Mustapha and Meddah, NacĂ©ra},
title = {Well ve-covered graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {},
number = {},
pages = {-},
year = {2023},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2023.28186.1469},
abstract = {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.},
keywords = {vertex-edge domination,independent vertex-edge domination,well ve-covered graphs,trees},
url = {https://comb-opt.azaruniv.ac.ir/article_14622.html},
eprint = {https://comb-opt.azaruniv.ac.ir/article_14622_6165a82d2ed9db6dfc8bf158a220335d.pdf}
}