Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2011-01-01

Journal: Utilitas Mathematica

Included Journals: Scopus

Volume: 84

Page Number: 273-285

ISSN: 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.