Computing the Zero Forcing Number for Generalized Petersen Graphs

Let G be a simple undirected graph with each vertex colored either white or black, u be a black vertex of G, and exactly one neighbor v of u be white. Then change the color of v to black. When this rule is applied, we say u forces v, and write u ® v . A zero forcing set of a graph G is a subset Z of vertices such that if initially the vertices in Z are colored black and remaining vertices are colored white, the entire graph G may be colored black by repeatedly applying the color-change rule. The zero forcing number of G, denoted Z(G), is the minimum size of a zero forcing set.In this paper, we investigate the zero forcing number for the generalized Petersen graphs (It is denoted by P(n,k)). We obtain upper and lower bounds for the zero forcing number for P(n,k). We show that Z(P(n,2))=6 for n ³ 10, Z(P(n,3))=8 for n ³ 12 and Z(P(2k+1,k))=6 for k ³ 5