THE SEMI-SPLITTING BLOCK GRAPHS WITH CROSSING NUMBERS THREE AND FORBIDDEN SUBGRAPHS FOR CROSSING NUMBER ONE

Let G = (V ,E) be a simple connected undirected graph with vertex set V and edge set E. The advent of graph theory has played a prominent role in wide variety of engineering applications. Minimization of crossing numbers in graphs optimizes its use in many applications. In this paper, we establish a necessary and sufficient condition for semi-splitting block graph to have crossing number 3.We deduce a necessary and sufficient condition for semi-splitting block graph to have crossing number 1 in terms of forbidden subgraphs.