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ON THE CROSSING NUMBER OF THE JOIN OF THE WHEEL ON FIVE VERTICES WITH THE DISCRETE GRAPH

Part of: Graph theory

Published online by Cambridge University Press:  21 November 2019

MICHAL STAŠ Open the ORCID record for MICHAL STAŠ [Opens in a new window]
MICHAL STAŠ*
Affiliation:
Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovak Republic email [email protected]
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Abstract

We give the crossing number of the join product $W_{4}+D_{n}$, where $W_{4}$ is the wheel on five vertices and $D_{n}$ consists of $n$ isolated vertices. The proof is based on calculating the minimum number of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph $W_{4}$ and from the set of subgraphs which cross the edges of $W_{4}$ exactly once.

Keywords

graphdrawingcrossing numberjoin productrotation

MSC classification

Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory
Secondary: 05C38: Paths and cycles
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 3 , June 2020 , pp. 353 - 361
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The research was supported by the internal faculty research project no. FEI-2017-39.

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