THE SEMI-SPLITTING BLOCK GRAPHS WITH CROSSING NUMBERS
V. R. KULLI
Department of Mathematics, Gulbarga University, Gulbarga-585106, Karnataka, India.
K. M. NIRANJAN *
Department of Mathematics, UBDTCE, Davangere - 577 004, Karnataka, India.
*Author to whom correspondence should be addressed.
Abstract
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 numbers 1 and 2.
Keywords: Semi-splitting, block, crossing number, planar, minimally nonouterplanar.