THE SEMI-SPLITTING BLOCK GRAPHS WITH CROSSING NUMBERS THREE AND FORBIDDEN SUBGRAPHS FOR CROSSING NUMBER ONE
K. M. NIRANJAN *
Department of Mathematics, UBDTCE, Davangere, 577 004, Karnataka, India.
RADHA R. IYER
Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Viswa Vidyapeetham, India.
M. S. BIRADAR
Department of Mathematics, Govt. First Grade College, Basavakalyan, 585 327, India.
DUPADAHALLI BASAVARAJA
Department of Mathematics, Govt. First Grade College, Harihara, 577 601, 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 number 3.We deduce a necessary and sufficient condition for semi-splitting block graph to have crossing number 1 in terms of forbidden subgraphs.
Keywords: Semi-splitting, block, crossing number, forbidden, planar, minimally nonouterplanar