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 Г of order n ≥ 2, Z[S(Г)] ≤ 2Z(Г) and also obtain many classes of graph in which Z[S(Г)] = 2Z(Г). Further, we show some classes of graphs in which Z[S(Г)] < 2Z(Г).