Maximal 3-γ-vertex-critical graphs

Abstract

Let γ(G) denote the minimum cardinality of a dominating set for G. A graph G is said to be κ-γ-vertex-critical if 7(G) = κ, but γ(G-v) < κ for each vertex v ε V(G) and G is maximal κ-γ-vertex-critical if G is κ-γ-vertex-critical and for each edge e ε E(G), -γ(G 4- e) < κ. In this paper, we characterize maximal 3-γ-vertex-critical graphs of connectivity two. It turns out that such graphs are factor-critical. We also provide sufficient conditions for maximal 3-γ-vertex-critical connected graph of even order to be bicritical.