The report for C<sub>60</sub>’s four dual Maximum Planar Graph’s all 4-colorings

Those Maximum Planar Graph whose vertex sequence 5<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup>6<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> has found four. They are Buckminsterfullerene -C₆₀’s dual Graph. Thus, C₆₀ exists in four primary forms at least. This paper bases on professor Shouchun Xu’s two algorithms, which are looking for batch of 4-coloring solution and using Kempe two color transform to generate 4-coloring trees, The integrated using of these two algorithms and got an algorithm to find low-order maximal planar graph’s all 4-colorings. This paper shows relevant findings for these four Maximum Planar Graph’s all 4-colorings .

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Publication Details

Published
2025-08-08
DOI
https://doi.org/10.1109/iaeac65194.2025.11166527
Primary Topic
Advanced Graph Theory Research
Type
article
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article

The report for C60’s four dual Maximum Planar Graph’s all 4-colorings

X. G. Cao, Shouchun Xu, Bin Cheng
Advanced Graph Theory Research
article

The report for C60’s four dual Maximum Planar Graph’s all 4-colorings

X. G. Cao, Shouchun Xu, Bin Cheng
article en

Abstract

Those Maximum Planar Graph whose vertex sequence 5<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup>6<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> has found four. They are Buckminsterfullerene -C₆₀’s dual Graph. Thus, C₆₀ exists in four primary forms at least. This paper bases on professor Shouchun Xu’s two algorithms, which are looking for batch of 4-coloring solution and using Kempe two color transform to generate 4-coloring trees, The integrated using of these two algorithms and got an algorithm to find low-order maximal planar graph’s all 4-colorings. This paper shows relevant findings for these four Maximum Planar Graph’s all 4-colorings .

Huanggang Normal University (CN), South Central Minzu University (CN)
Openalex Percentile: Top 73%
Advanced Graph Theory Research
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