关键词: 点临界, 全控制集, 全控制数, 冠图, Cayley 图

Abstract:

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than that of G. These graphs are called γ_t-critical. If such a graph G has total domination number k,  it is called k-γ_t-critical. In this paper, the authors give the structure proof of those graphs satisfying n=Δ(G)(γ_t(G)-1)+1.