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On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph

Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia
Symmetry 2020, 12(1), 135; https://doi.org/10.3390/sym12010135
Received: 19 December 2019 / Accepted: 19 December 2019 / Published: 9 January 2020
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
In the paper, we extend known results concerning crossing numbers of join products of small graphs of order six with discrete graphs. The crossing number of the join product G * + D n for the graph G * on six vertices consists of one vertex which is adjacent with three non-consecutive vertices of the 5-cycle. The proofs were based on the idea of establishing minimum values of crossings between two different subgraphs that cross the edges of the graph G * exactly once. These minimum symmetrical values are described in the individual symmetric tables.
Keywords: graph; good drawing; crossing number; join product; cyclic permutation graph; good drawing; crossing number; join product; cyclic permutation
MDPI and ACS Style

Staš, M. On the Crossing Numbers of the Joining of a Specific Graph on Six Vertices with the Discrete Graph. Symmetry 2020, 12, 135.

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