INDEPENDENT ۲-DOMINATION POLYNOMIALS IN THE GRAPH Cn

Let G (V,E) be a simple graph. A subset W C V is called an independent ۲-dominating set if the vertices in W are pairwise non-adjacent and every vertex in V \ W has at least two neighbors in W. The independent ۲-domination polynomial of a graph G, denoted by D½ ۳ (G, x), is the generating function in which the coefficient of xk counts the number of independent ۲-dominating sets of size k. In this paper, we compute the independent ۲-domination polynomial for the cycle graph Cn. We derive closed formulas for this polynomial in both cases where n is even or odd. Furthermore, we analyze the structural constraints that determine the existence of independent ۲-dominating sets in cycles and enumerate them based on their cardinality. Our results enrich the study of domination-type polynomials in symmetric and periodic graph structures.

کلیدواژه ها:

Independent ۲-dominating sets ، independent ۲-domination number ، independent ۲-domination polynomial ، Cycle graph