DETERMINING CROSSING NUMBERS OF GRAPHS OF ORDER SIX USING CYCLIC PERMUTATIONS
Michal Staš · Bulletin of the Australian Mathematical Society · 2018
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.