The crossing numbers of several 
			graphs of order eight with paths

Emilia Drazenska

doi:10.26456/mmg/2019-723

The crossing numbers of several graphs of order eight with paths

Mathematical Modelling and Geometry ◽

10.26456/mmg/2019-723 ◽

2019 ◽

Vol 7 (2) ◽

Author(s):

Emilia Drazenska

Keyword(s):

Crossing Numbers

Download Full-text

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

Mathematics ◽

10.3390/math9111277 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1277

Author(s):

Michal Staš

Keyword(s):

Connected Graph ◽

Crossing Numbers ◽

Tripartite Graph ◽

Complete Tripartite Graph

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 K1,1,3\e obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph K1,1,3. 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.

Download Full-text

Cyclic permutations and crossing numbers of join products of two symmetric graphs of order six

Carpathian Journal of Mathematics ◽

10.37193/cjm.2019.02.02 ◽

2019 ◽

Vol 35 (2) ◽

pp. 137-146

Author(s):

STEFAN BEREZNY ◽

MICHAL STAS ◽

◽

Keyword(s):

Crossing Number ◽

Crossing Numbers ◽

Symmetric Graphs ◽

Isolated Vertex ◽

Join Of Graphs ◽

Discrete Graph

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 + Dn, where the graph G consists of one 5-cycle and of one isolated vertex, and Dn consists on n isolated vertices. The proof is done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all vertices of the graph. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph Dn and with the path Pn on n vertices for other two graphs.

Download Full-text