Join Product: An operation on two graphs that connects every vertex of one graph with every vertex of the other, forming a new combined graph. Path: A sequence of distinct vertices in a graph ...

Let G be a graph. The splitting graph SP (G) of G is the graph received from G by putting a new vertex w′ for each w ∈ VG and joining w′ to all vertices of G adjacent to w. Let SG be the set of such ...

The crossing number cr (G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. In the paper, the crossing number of the join product G∗ + Dn for the connected ...