On the zero forcing number of graphs and their splitting graphs

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 $Z[S(\Gamma)] < 2 Z(\Gamma)$.