On the zero forcing number of some Cayley graphs
Ebrahim Vatandoost, Yasser Golkhandy Pour · Algebraic structures and their applications · 2017
Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Z\subseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the color of all vertices Γ in to black. The zero forcing number of Γ is the minimum of |Z| over all zero forcing sets for Γ and is denoted by Z(Γ). In this paper, we consider the zero forcing number of some families of Cayley graphs. In this regard, we show that Z(Cay(D2n,S))=2|S|-2, where D2n is dihedral group of order 2n and S={a, a3, ... , a2k-1, b}. Also, we obtain Z(Cay(G,S)), where G= is a cyclic group of even order n and S={ai : 1≤ i≤ n and i is odd}, S={ai :1≤ i≤ n and i is odd}\{ak,a-k} or |S|=3.