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Lemańska M., Rodríguez-Velázquez J. A., Trujillo-Rasua R.

Fundamenta Informaticae

2017

Vol. 152, nr 3

273--287

A vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The vertex cover number τ(G) is the minimum cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]ω = (N[D], Eω) weakly induced by D, is connected, where Eω is the set of all edges having at least one vertex in D. The weakly connected domination number γω(G) of G is the minimum cardinality among all weakly connected dominating sets of G. In this article we characterize the graphs where γω(G) = τ(G). In particular, we focus our attention on bipartite graphs, regular graphs, unicyclic graphs, block graphs and corona graphs.