Opuscula Math. 40, no. 3 (2020), 383-397
https://doi.org/10.7494/OpMath.2020.40.3.383

 
Opuscula Mathematica

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

Michal Staš

Abstract. 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.

Keywords: graph, drawing, crossing number, join product, cyclic permutation.

Mathematics Subject Classification: 05C10, 05C38.

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  • Michal Staš
  • ORCID iD https://orcid.org/0000-0002-2837-8879
  • Technical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics and Theoretical Informatics, 042 00 Košice, Slovak Republic
  • Communicated by Ingo Schiermeyer.
  • Received: 2019-06-26.
  • Revised: 2020-01-18.
  • Accepted: 2020-02-25.
  • Published online: 2020-04-04.
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Cite this article as:
Michal Staš, On the crossing numbers of join products of five graphs of order six with the discrete graph, Opuscula Math. 40, no. 3 (2020), 383-397, https://doi.org/10.7494/OpMath.2020.40.3.383

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