More on co-even domination number

TL;DR

This paper investigates the co-even domination number in graphs, exploring its properties and counting co-even dominating sets for specific graph classes to deepen understanding of this graph parameter.

Contribution

It provides new results on the co-even domination number and counts co-even dominating sets in particular graphs, expanding the theoretical framework.

Findings

Derived bounds for co-even domination number

Counted co-even dominating sets in specific graphs

Extended understanding of co-even domination properties

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 find more results on co-even domination number of graphs and count the number of co-even dominating sets of some specific graphs.