Perfect domination number of path graph Pn and its Corona product with another path graph Pn−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 path graphs and obtained their perfect domination number we also trying to find a corona product of path graph Pn with path graph Pn−1 and as a conclusion we give such applications of it.