The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

Mathematics

卷:9

Michal Staš¹ 

[1] Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia;

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

DOI  :  10.3390/math9111277

来源: DOAJ

【 摘 要 】

The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph $K_{1,1,3}\backslash e$ obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph $K_{1,1,3}$. The proofs are done with the help of well-known exact values for the crossing numbers of the join products of subgraphs of the considered graph with paths and cycles. Finally, by adding some edges to the graph under consideration, we obtain the crossing numbers of the join products of other graphs with the paths and the cycles on n vertices.

【 授权许可】

Unknown