On Stratification and Domination in Prisms

Abstract

A graph G is 2-stratified if its vertex set partitioned into two color classes. We color the vertices in one color class red and the other class blue. Let F be a 2-stratified graph with one fixed blue vertex v specified. We say that F is rooted at v. The F-domination number of a graph G is the minimum number of red vertices of G in a red- blue coloring of the vertices of G such that every blue vertex v of G belongs to a copy of F rooted at v. In this paper we investigate the F- domination number of prisms when F is 2-stratified 6-cycle rooted at a blue vertex. And we get a new generalization result of stratified domination number for prisms.