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Total complementary acyclic domination in graphs

Journal: International Journal of Mathematics and Soft Computing (Vol.3, No. 2)

Publication Date:

Authors : ;

Page : 5-9

Keywords : Domination; total domination; total complementary acyclic dominating set; total complementary acyclic domination number;

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Abstract

Let $G=(V,E)$ be a graph without isolates. A subset $S$ of $V(G)$ is called a total dominating set of $G$ if for every $vin V$, there exists $uin S$ such that $u$ and $v$ are adjacent. $S$ is called a total complementary acyclic dominating set of $G$, if $S$ is a total dominating set of $G$ and $leftlangle V-Srightrangle$ is acyclic. $V(G)$ is a total complementary acyclic dominating set of $G$ (since $G$ has no isolates). The minimum cardinality of a total complementary acyclic dominating set of $G$ is called the total complementary acyclic domination number of $G$ and is denoted by $gamma_{c-a}^{t}(G)$. In this paper, characterization of graphs for which $gamma_{c-a}^{t}(G)$ takes specific values are found.

Last modified: 2013-08-24 12:25:06