On the crossing numbers of join products of five graphs of order six with the discrete graph

Opuscula Mathematica

article

Michal Staš¹ 

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

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

DOI  :  10.7494/OpMath.2020.40.3.383

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC