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The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

MATHEMATICS (2021)

Cyclic Permutations in Determining Crossing Numbers

Marian Klesc et al.

Summary: The paper focuses on the crossing number problem of graphs, particularly the crossing numbers of join products of graphs. By extending existing results, the crossing numbers of join products of small graphs with discrete graphs are given. The crossing numbers of other types of join products are also provided. The methods used in this study are new and based on combinatorial properties of cyclic permutations.

DISCUSSIONES MATHEMATICAE GRAPH THEORY (2022)

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Article Mathematics, Applied

ON THE CROSSING NUMBERS OF JOIN PRODUCTS OF W4+Pn AND W4+Cn

Michal Stas et al.

Summary: This paper focuses on determining the crossing number of graphs involving a wheel W-4 and path/cycle P-n/C-n, and proves a conjecture while also proposing a new one. The conjecture regarding the crossing number of W-3 + C-n was recently proven, and this paper extends the validity to W-4 + C-n, also introducing a new conjecture for W-m + P-n.

OPUSCULA MATHEMATICA (2021)

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Article Mathematics