On Maximum Total Domination Vertex Critical Graphs

A set S of vertices in a graph G is a dominating set(total dominating set)of G if each vertex of V(G)-S(V(G))is adjacent to some vertex of S(other than itself).The minimum cardinality among all dominating sets(total dominating sets)of G is called the domination(total domination)number of G,denoted by γ(G)(γ_t(G)).In this paper,we characterize the γ_t-critical graphs with γ_t(G)=n-Δ(G),which answers a question proposed by Goddard et al.