Co-even domination number of a modified graph by operations on a vertex or an edge

Document Type : Original Article

Authors

1 Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran

2 Department of Mathematics, Technical and Vocational University, Tehran, Iran

Abstract

Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V-D$. The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$. In this paper, we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 29 June 2024

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