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Determining Crossing Number of Join of the Discrete Graph with Two Symmetric Graphs of Order Five

Faculty of Electrical Engineering and Informatics, Technical University of Košice, 040 01 Košice, Slovakia
Symmetry 2019, 11(2), 123; https://doi.org/10.3390/sym11020123
Received: 19 December 2018 / Revised: 17 January 2019 / Accepted: 18 January 2019 / Published: 22 January 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

The main aim of the paper is to give the crossing number of the join product G + D n for the disconnected graph G of order five consisting of one isolated vertex and of one vertex incident with some vertex of the three-cycle, and D n consists of n isolated vertices. In the proofs, the idea of the new representation of the minimum numbers of crossings between two different subgraphs that do not cross the edges of the graph G by the graph of configurations G D in the considered drawing D of G + D n will be used. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph D n and with the path P n on n vertices for three other graphs. View Full-Text
Keywords: graph; good drawing; crossing number; join product; cyclic permutation graph; good drawing; crossing number; join product; cyclic permutation
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Staš, M. Determining Crossing Number of Join of the Discrete Graph with Two Symmetric Graphs of Order Five. Symmetry 2019, 11, 123.

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