The Crossing Numbers of Join of Paths and Cycles with Two Graphs of Order Five

摘要

The crossing number cr(G) of a graph G is the minimal num ber of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There are collected the exact values of crossing num bers for join of all graphs of at most four vertices with paths and cycles. In the paper, we extend these results. For two special graphs G on five vertices, we give the crossing numbers of the join products G + D_n, G + P_n, and G + C_n, where D_n consists on n isolated vertices, P_n and C_n are the path and cycle on n vertices, respectively.