@Article{Staš2022,
author = "Staš, Michal and Švecová, Mária",
title = "The crossing numbers of join products of paths with three graphs of order five",
journal = "Opuscula Math.",
year = "2022",
volume = "42",
number = "4",
pages = "635--651",
doi = "https://doi.org/10.7494/OpMath.2022.42.4.635",
url = "https://doi.org/10.7494/OpMath.2022.42.4.635",
abstract = "The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices. The proofs are done with the help of a lot of well-known exact values for the crossing numbers of the join products of subgraphs of the graph \(G^\ast\) with the paths. Finally, by adding new edges to the graph \(G^\ast\), we are able to obtain the crossing numbers of the join products of two other graphs with the path \(P_n\).",
keywords = "graph, crossing number, join product, cyclic permutation, path",
issn = "1232-9274"
}