On the Zero Forcing Number of Some Cayley Graphs

‎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 zsubseteq 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, ‎a^3‎, ‎... ‎, ‎a^2k1‎, ‎b}. ‎also‎, ‎we obtain z(cay(g,s))‎, ‎where g=< a> is a cyclic group of even order n and s={a^i :‎ 1≤ i≤ n‎ and i is odd}‎, ‎s={a^i‎ :‎1≤ i≤ n‎ and i is odd}{a^k,a^-k} or |s|=3‎.