Crossing numbers of join product of several graphs on 6 vertices with path using cyclic permutation

The crossing number, cr (G), of a simple graph G is the minimum number of edge crossings in a good drawing of G in the plane. In general, compute the crossing number for a given graph is a very difficult problem. The crossing numbers of a few families of graphs are known. One of them are join products of special graphs. Exact values of crossing numbers of the join products of graph G with discrete graph D-n, path P-n or cycle C-n are known for several graphs G. In the paper, we extend known results concerning crossing numbers for join of two graphs of order six with path P-n.