Parity Properties of Configurations

Michal Staš
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Michal Staš: Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia

Mathematics, 2022, vol. 10, issue 12, 1-14

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 .

Keywords: graph; join product; crossing number; configuration; parity properties; path; cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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