On the crossing numbers of the join products of five graphs on six vertices with discrete graphs

Berežný, Štefan and Staš, Michal 

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The crossing number \mathrm{cr}(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. In the paper, the crossing number of the join product G^\ast + D_n for the connected graph G^\ast on six vertices consisting of one path on four vertices P_4 and two leaves adjacent with the same outer vertex of the path P_4 is given, where D_n consists of n isolated vertices. Finally, by adding some edges to the graph G^\ast, we obtain the crossing numbers of the join products of other four graphs with D_n.


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Berežný, Štefan, Staš, Michal