@Article{Staš2020,
author = "Staš, Michal",
title = "On the crossing numbers of join products of five graphs of order six with the discrete graph",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "3",
pages = "383--397",
doi = "https://doi.org/10.7494/OpMath.2020.40.3.383",
url = "https://doi.org/10.7494/OpMath.2020.40.3.383",
abstract = "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 \(G^{\ast} + D_n\), where the disconnected graph \(G^{\ast}\) of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the \(5\)-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph \(G^{\ast}\), the crossing numbers of \(G_i+D_n\) for four other graphs \(G_i\) of order six will be also established.",
keywords = "graph, drawing, crossing number, join product, cyclic permutation",
issn = "1232-9274"
}