Domination Number and Total Domination Number of Square of Normal Product of Cycles

Abstract

In 1958-Claude Berge introduced the domination number of a graph which is utilized to secure the single vertices. A set $S\subseteq V(G)$ is a dominating set of $G$ if every vertex of $V(G)-S$ is adjacent to at least one vertex of $S$. The cardinality of the smallest dominating set of $G$ is called the domination number of $G$. A dominating set $S$ is called total dominating set if the induced subgraph $\langle S\rangle$ has no isolated vertex. The square $G^2$ of a graph $G$ is obtained from $G$ by adding new edges between every two vertices having distance $2$ in $G$. In this paper, we determine the domination number and total domination number of square of normal product of cycle graphs by evaluating their minimum dominating set and minimum total dominating set and short display are also provided to understand the results.