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r个点并圈的补图的色等价图类
The Chromatic Equivalence Classes of the Complements of Union Graphs of r Vertices and a Cycle

DOI: 10.12677/PM.2021.116125, PP. 1112-1120

Keywords: 色多项式，伴随多项式，色等价，伴随等价，色唯一，伴随唯一
Chromatic Polynomial, Adjoint Polynomial, Chromatically Equivalent, Adjointly Equivalent, Chromatically Unique, Adjointly Unique

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Abstract:

两个图G 和H 色等价当且仅当它们的补图伴随等价. 图G 色唯一当且仅当G 伴随唯一. 在这篇文章中, 我们计算了rK1UCm(r ≥ 1, m ≥ 3) 的伴随等价图的个数, 并刻画了它的伴随等价图类. 因而, 我们也计算了rK1UCm的色等价图的个数, 刻画了rK1UCm的色等价图类.
Two graphs G and H are chromatically equivalent if and only if G and H are adjointly equivalent. G is chromatically unique if and only if G adjointly unique. In this paper, the number of the adjoint equivalence graphs of rK1UCm(r ≥ 1, m ≥ 3) is calculated, and the adjoint equivalence classes of rK1UCm can also be characterized. As a result, the number of the chromatic equivalence graphs of rK1UCm is calculated, and the chromatic equivalence classes of rK1UCm can also be characterized.

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