Zero Forcing Number of F-Sum of Some Families of Graphs

Abstract

This thesis deals with zero forcing number of 𝐹-sum of graphs derived from certain families of graph. A zero forcing set of graph 𝑆 is a set 𝑆 ⊆ 𝑉 such that there are no white vertices in the derived coloring of 𝑆. The zero forcing number of 𝐺 is 𝑍(𝐺) = min⁡{|𝑆|: 𝑆⁡is zero forcing set of⁡𝐺}. We study zero forcing number of 𝐹-sum of two path graph, two cycle graph and then path and cycle graph. It has been proved that it is constant in case of 𝑆 operation of 𝐹-sum and unbounded otherwise.