## 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.

#### How to Cite

*Asian Journal of Current Research*,

*5*(1), 9–16. Retrieved from https://ikprress.org/index.php/AJOCR/article/view/5214

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