A note on the stratified domination number of generalized planar Petersen like graphs

Abstract

Let G be a graph with the vertex set V (G). G is called 2-stratified if V (G) is partitioned into red and blue vertices. The stratified domination number of a graph G is the minimum number of red vertices of V (G) in a red-blue coloring of the vertices of V (G) such that every blue vertex v of V (G) lies in a vuw (blue, blue, red) path in G for a blue vertex u ∈ V (G) (u 6= v) and a red vertex w ∈ V (G). In this paper we first define the concept of generalized planar Petersen like graphs PP(n,2) for any positive odd integers and study the stratified domination number of generalized planar Petersen like graphs