Vatandoost, E., Golkhandy Pour, Y. (2017). On the zero forcing number of some Cayley graphs. Algebraic Structures and Their Applications, 4(2), 15-25. doi: 10.29252/asta.4.2.15

Ebrahim Vatandoost; Yasser Golkhandy Pour. "On the zero forcing number of some Cayley graphs". Algebraic Structures and Their Applications, 4, 2, 2017, 15-25. doi: 10.29252/asta.4.2.15

Vatandoost, E., Golkhandy Pour, Y. (2017). 'On the zero forcing number of some Cayley graphs', Algebraic Structures and Their Applications, 4(2), pp. 15-25. doi: 10.29252/asta.4.2.15

Vatandoost, E., Golkhandy Pour, Y. On the zero forcing number of some Cayley graphs. Algebraic Structures and Their Applications, 2017; 4(2): 15-25. doi: 10.29252/asta.4.2.15

^{1}Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran

^{2}Department of Mathematics, Faculty of sciences, Imam Khomeini International University, Qazvin, Iran

Abstract

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(D_{2n},S))=2|S|-2, where D_{2n} is dihedral group of order 2n and S={a, a^{3}, ... , a^{2k-1}, 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.

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