On graphs with equal domination and covering numbers (Q1329822)

A set \(D\) of vertices of a simple graph \(G\) is dominating if every vertex in \(V(G)- D\) is adjacent to some vertex in \(D\), and covering if every edge of \(G\) has at least one end in \(D\). The domination number \(\gamma(G)\) is the minimum order of a dominating set in \(G\). The covering number \(\beta(G)\) is the minimum order of a covering set in \(G\). In this paper, the author characterizes regular graphs, cactus graphs without cycles of length four, chordal graphs, and unicyclic graphs \(G\) for which \(\gamma(G)= \beta(G)\).