The crossing numbers of join products of paths with three graphs of order five

Opuscula Mathematica

article

Michal Staš (corresponding author)¹  Mária Švecová¹ 

[1] Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics and Theoretical Informatics

关键词: graph;    crossing number;    join product;    cyclic permutation;    path.;   

DOI  :  10.7494/OpMath.2022.42.4.635

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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 \(P_n\).

【 授权许可】

CC BY-NC