On the zero forcing number of graphs and their splitting graphs

Abstract

In [10], the notion of the splitting graph of a~graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph \(\Gamma\) of order \(n \ge 2\), \(Z[S(\Gamma)]\le 2 Z(\Gamma)\) and also obtain many classes of graph in which \(Z[S(\Gamma)]= 2 Z(\Gamma)\). Further, we show some classes of graphs in which \(Z[S(\Gamma)] < 2 Z(\Gamma)\).