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DETERMINING CROSSING NUMBERS OF GRAPHS OF ORDER SIX USING CYCLIC PERMUTATIONS

Published online by Cambridge University Press:  17 August 2018

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 michal.stas@tuke.sk
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Abstract

We extend known results concerning crossing numbers by giving the crossing number of the join product $G+D_{n}$ , where the connected graph $G$ consists of one $4$ -cycle and of two leaves incident with the same vertex of the $4$ -cycle, and $D_{n}$ consists of $n$ isolated vertices. The proofs are done with the help of software that generates all cyclic permutations for a given number $k$ and creates a graph for calculating the distances between all $(k-1)!$ vertices of the graph.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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Footnotes

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

References

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