Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2011-03-01

Journal: UTILITAS MATHEMATICA

Included Journals: SCIE

Volume: 84

Page Number: 273-285

ISSN: 0315-3681

Key Words: Total domination number; gamma(t)-critical graph; Vertex critical graph

Abstract: 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.