On the zero forcing number of some Cayley graphs

ýLet Γa be a graph whose each vertex is colored either white or blacký. ýIf u is a black vertex of Γ such that exactly one neighborý ýv of u is whiteý, ýthen u changes the color of v to blacký. ýA zero forcing set for a Γ graph is a subset of vertices Z\subseteq V(Γ) such thatý if initially the vertices in Z are colored black and the remaining vertices are colored whiteý, ýthen Z changes the color of all vertices Γ in to blacký. ýThe zero forcing number of Γ is the minimum of |Z| over all zero forcing sets for Γ and is denoted by Z(Γ)ý. In this paperý, ýwe consider the zero forcing number of some families of Cayley graphsý. ýIn this regardý, ýwe show that Z(Cay(D2n,S))=2|S|-2ý, ýwhere D2n is dihedral group of order 2n and S={aý, ýa3ý, ý... ý, ýa2k-1ý, ýb}. ýAlsoý, ýwe obtain Z(Cay(G,S))ý, ýwhere G= is a cyclic group of even order n and S={ai :ý 1≤ i≤ ný and i is odd}ý, ýS={aiý :ý1≤ i≤ ný and i is odd}\{ak,a-k} or |S|=3ý.