vertices, for p odd. has shown however t e of graphs on PO vertices whose construction was described in [ 11. search was na o other graph with this chromatic polynomial was found. es
The chromatic uniqueness of W10
โ Scribed by Nian-Zu Li; Earl Glen Whitehead Jr
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 165 KB
- Volume
- 104
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
Li, N.-Z. and E.G. Whitehead Jr, The chromatic uniqueness of W,,, Discrete Mathematics 104 (1992) 197-199. Xu and Li proved the chromatic uniqueness of wheels on an odd number of vertices. It is known that the wheels on six vertices and eight vertices are not chromatically unique. Read found that the wheel on ten vertices is chromatically unique by computer computations.
Here, we sketch a mathematical proof of the chromatic uniqueness of the wheel on ten vertices.
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## Abstract A graph is chromatically unique if it is uniquely determined by its chromatic polynomial. Let __G__ be a chromatically unique graph and let __K__~__m__~ denote the complete graph on __m__ vertices. This paper is mainly concerned with the chromaticity of __K__~__m__~ + __G__ where + deno