Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by γrt(G), is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.

Publication Year

2012

Journal Title

Discussiones Mathematicae Graph Theory

Volume number

32

Issue number

4

Publisher

De Gruyter Open

First Page (page number)

629

Last Page (page number)

641

Referreed

1

DOI

10.7151/dmgt.1632

ISSN (print)

20835892

Keywords

total domination number, total restrained domination number, direct product of graphs

Included in

Mathematics Commons

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