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ON DOMINATION OF THE TOTAL GRAPH ASSOCIATED TO $\Gamma$-SEMIGROUP OF $\mathbb{Z}_n$
Keywords:
the total graph, $\Gamma$-semigroup, domination number.DOI:
https://doi.org/10.17654/0974165822016Abstract
We choose two non-empty sets $\mathbb{Z}_n(n \geq 2)$ and $\Gamma=U_n$. This set $\mathbb{Z}_n$ forms a $\Gamma$-semigroup. The undirected graph of "Total graph associated to $\Gamma$-semigroup of $\mathbb{Z}_n$ " represented by $G\left(\mathbb{Z}_n(\Gamma)\right)$ is a simple graph where any two distinct vertices $x$ and $y$ of $\mathbb{Z}_n$ are made to be adjacent if and only if $x+\alpha+y \equiv 0(\bmod n)$. This paper focuses on determining the domination number of the graph structure given by $G\left(\mathbb{Z}_n(\Gamma)\right)$ for various values of $n$.
Received: November 10, 2021
Accepted: February 19, 2022
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