Cyclic permutations and crossing numbers of join products of two symmetric graphs of order six

Berežný, Štefan and Staš, Michal



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The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G + D_n, where the graph G consists of one 5-cycle and of one isolated vertex, and D_n consists on n isolated vertices. The proof is done with the~help of software that generates all cyclic permutations for a given number k, and creates a~new graph {COG} for calculating the distances between all (k-1)! vertices of the graph. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph D_n and with the path P_n on n vertices for other two graphs.



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Staš, Michal, Berežný, Štefan