2023
DOI: 10.1051/ro/2023074
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Graphs with unique minimum vertex-edge dominating sets

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 ⊆ 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 of S . The vertex-edge domination number is the minimum cardinality of a ved–set in G. In this paper, we investigate the graphs having unique minimum ved-sets that we will call UVED-graphs. We start by giving some basic propert… Show more

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