Abstract
In the paper, the crossing number of the join product \(G^* + D_n\) for the disconnected graph \(G^*\) consisting of one isolated vertex and of one component isomorphic to \(K_{1,1,2}\) is given. Moreover, the crossing numbers of \(H_i + D_n\) for three other graphs \(H_i\) of order five are also established. These results extend a small number of known results concerning crossing numbers of join products. The methods used in the paper are new. They are based on combinatorial properties of cyclic permutations.
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The authors thank the reviewer for their extremely careful reading of the whole text and for his useful suggestions.
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Klešč, M., Staš, M. & Petrillová, J. The Crossing Numbers of Join of Special Disconnected Graph on Five Vertices with Discrete Graphs. Graphs and Combinatorics 38, 35 (2022). https://doi.org/10.1007/s00373-021-02423-5
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DOI: https://doi.org/10.1007/s00373-021-02423-5