On the Zero Forcing Number of Complementary Prism Graphs

Document Type : Original paper


1 Department of Mathematics, CHRIST(Deemed to be University) Bangalore India

2 Department of Mathematics CHRIST(Deemed to be University) Bangalore India


The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph $G$.  The aim of this article is to compute the zero forcing number of complementary prism graphs.  Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result.  Let $G$ and $\overline{G }$ be connected graphs. Then $Z(G\overline{G})\leq n-1$ if and only if  there exists two vertices $v_i,v_j \in V(G)$ and $i\neq j$ such that, either $N(v_i) \subseteq N(v_j)$ or $N[v_i] \subseteq N[v_j]$ in $G$.


Main Subjects

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