On the Zero Forcing Number of Complementary Prism Graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, CHRIST (Deemed to be university), Bengaluru-560029, Karnataka, India

2 Department of Mathematics, RV College of Engineering, Bengaluru-560059, Karnataka, India

Abstract

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 $G$.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 25 December 2023

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