Perfect Domination Number of a Cycle graph 𝑪𝒏 and its Corona product with another Cycle graph 𝑪𝒏-𝟏

Abstract

According to the research paper on Perfect Dominating Sets by Marilynn Livingston and Quentin F. stout[1]they have been constructed the PDSs in families of graphs arising from the interconnected networks of parallel computers also contained perfect domination numbers of trees, dags, series-parallel graphs, meshes, tori, hypercubes, cube connected cycles and de Bruijin graphs and give linear algorithms for determining if a PDS exist, and generate a PDS when one does. They also proved that 2 and 3-dimensional hypercube graph having infinitely many PDSs. In this paper we are trying to apply their concept on cycle graphs and obtained their perfect domination number we also trying to find such applications of it.