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Indexed by:期刊论文

Date of Publication:2011-01-01

Journal:Utilitas Mathematica

Included Journals:Scopus

Volume:84

Page Number:273-285

ISSN No.:03153681

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