ON GRAPHS WITH EQUAL DOMINATION AND COVERING NUMBERS

A set D of vertices of a simple graph G is dominating if every vertex not in D is adjacent to some vertex in D, and covering if every edge o f G has at least one end in D. The domination number gamma(G) is the m inimum order of a dominating set in G. The covering number beta(G) is the minimum order of a covering set in G. We characterize regular grap hs, cactus graphs without cycles of length four, chordal graphs, and u nicyclic graphs G for which gamma(G) = beta(G).