The crossing number of Cartesian product of sunlet graph with path and complete bipartite graph.

The crossing number of a graph G , denoted by cr (G) , is defined to be the minimum number of crossings that arise among all its drawings in the plane. This concept has been of interest to many researchers who have studied it for many families of graphs. In this paper, we introduce the crossing number of Cartesian product of sunlet graph S m with path P n . Further, we prove that the crossing number of S m □ P 2 is equal to m , along with giving a conjecture for the general case. In addition, we utilize the vertex's rotation concept in order to prove some necessary conditions for the complete bipartite graph K m , n to be optimal when it is drawn in the plane, by presenting an upper bound for the crossing number of any subgraph in it together with determining the exact number of crossings in case the vertices of subgraph have the same rotation. [ABSTRACT FROM AUTHOR]