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Parity Properties of Configurations

Author

Listed:
  • Michal Staš

    (Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia)

Abstract

In the paper, the crossing number of the join product G * + D n for the disconnected graph G * consisting of two components isomorphic to K 2 and K 3 is given, where D n consists of n isolated vertices. Presented proofs are completed with the help of the graph of configurations that is a graphical representation of minimum numbers of crossings between two different subgraphs whose edges do not cross the edges of G * . For the first time, multiple symmetry between configurations are presented as parity properties. We also determine crossing numbers of join products of G * with paths P n and cycles C n on n vertices by adding new edges joining vertices of D n .

Suggested Citation

  • Michal Staš, 2022. "Parity Properties of Configurations," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1998-:d:835317
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