On total domination and total equitable domination in graphs

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Authors :

S. K. Vaidya 1 * and A. D. Parmar 2

Author Address :

1Department of Mathematics, Saurashtra University, Rajkot - 360 005, Gujarat, India.
2Atmiya Institute of Technology and Science for Diploma Studies, Rajkot - 360 005, Gujarat, India.

*Corresponding author.

Abstract :

A dominating set $D$ of a graph $G$ is called total if every vertex of $V(G)$ is adjacent to at least one vertex of $D$, equivalently if $N(D) = V(G)$ then $D$ is called total dominating set. A dominating set $D$ is called total equitable dominating set if it is total and for every vertex in $V(G) - D$ there exists a vertex in $D$ such that they are adjacent and difference between their degrees is at most one. The minimum cardinality of a total (total equitable) dominating set is called total (total equitable) domination number of $G$ which is denoted by $gamma _t (G)$($gamma _t^e(G)$). We have investigated exact value of these parameters for some graphs.

Keywords :

Dominating set, total dominating set, equitable dominating set.



Article Info :

Received : November 12, 2017; Accepted : March 23, 2018.



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