Domination Parameters on Regular Graphs of the Commutative Ring $Z_{n}$

Abstract

In 1891 the Danish mathematician Julius Petersen (1839-1910) published a paper on the factorization of~regular graphs. This was the first paper in the history of mathematics to contain fundamental results explicitly in graph theory. A regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular graph with vertices of degree \textit{k} is called a \textit{k}-regular graph or regular graph of degree \textit{k}. In this paper our main aim is to find out the dominating parameters of Regular graph obtained on the Commutative ring of type $Z_{n}$. A subset D of V is said to be a dominating set of G if every vertex in $V-D$ is adjacent to a vertex in D. We determine the domination parameters i.e., domination number, dominating set and Minimum domination number of Regular graphs of the commutative ring $Z_{n}$.