DETERMINING CROSSING NUMBERS OF GRAPHS OF ORDER SIX USING CYCLIC PERMUTATIONS

Abstract

We extend known results concerning crossing numbers by giving the crossing number of the join product$G+D_{n}$, where the connected graph$G$consists of one$4$-cycle and of two leaves incident with the same vertex of the$4$-cycle, and$D_{n}$consists of$n$isolated vertices. The proofs are done with the help of software that generates all cyclic permutations for a given number$k$and creates a graph for calculating the distances between all$(k-1)!$vertices of the graph.