Dominating sets and polynomial of equality co-neighborhood domination of graphs
Sahib Sh. Kahat, Manal Naji Al-harere · AIP conference proceedings · 2022
Let G = (V, E) be a simple and undirected graph, which has no isolated vertices. A proper subset D⊂V is called the equality co-neighborhood dominating set of G (ENDS), if ∀ v∈D has equally number of neighborhood vertices in the set V – D. In this paper, by using the new definition (ENDS) the Gn−1i, is constructed and the recursive formula for den(Gn, i) is obtained. The polynomial Den (Gn,x)=∑i=1n−1den(Gn,i)xi, (equality co-neighborhood domination polynomial) for some graphs with some properties of this polynomial is determined.