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论文类型：期刊论文

发表时间：2011-03-01

发表刊物：UTILITAS MATHEMATICA

收录刊物：SCIE

卷号：84

页面范围：273-285

ISSN号：0315-3681

关键字：Total domination number; gamma(t)-critical graph; Vertex critical graph

摘要：Let gamma(t)(C) be the total domination number of graph G, a graph G is k-total domination vertex critical (or just k-gamma(t)-critical) if gamma(t)(C) = k, and for any vertex v of G that is not adjacent to a vertex of degree one, gamma(t)(G - v) = k - 1. Mojdeh and Rad [6] proposed an open problem: Does there exist a 3-gamma(t)-critical graph G of order Delta(G) + 3 with Delta(G) odd? In this paper, we prove that there exists a 3-gamma(t)-critical graph G of order Delta(G) + 3 with odd Delta(G) >= 9.