ΦS-型圖簇的伴隨分解及其色性分析

索南仁欠,李生剛

(1.陜西師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,陜西西安 710062;2.青海師范大學(xué)數(shù)學(xué)系,青海西寧 810008)

ΦS-型圖簇的伴隨分解及其色性分析

索南仁欠1,2,李生剛1

(1.陜西師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院,陜西西安 710062;2.青海師范大學(xué)數(shù)學(xué)系,青海西寧 810008)

運(yùn)用圖的伴隨多項(xiàng)式的性質(zhì),討論了圖簇ΦS((kn+1)σ,nσ)∪2kSσ的伴隨多項(xiàng)式的因式分解定理,進(jìn)而證明了它們的補(bǔ)圖的色等價(jià)性.

色多項(xiàng)式;伴隨多項(xiàng)式;因式分解;色等價(jià)性

1 預(yù)備知識(shí)及準(zhǔn)備工作

圖1

圖2

圖3 ΨS(kσ,nσ)

圖4 ΦS((kn+1)σ,nσ)

2 因式分解定理

3 色等價(jià)性分析

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The factorization of adjoin polynomials of graphs of ΦS-shape and chromatic non-uniqueness analysis

Suonan Renqian1,2,Li Shenggang1

(1.College of Mathematics and Information science,Shanxi normal university,Xi′an710062,China;
2.Department of Mathematics,Qinghai Normal University,Xining810008,China)

By applying the properties of adjoint polynomials,We prove that factorization theorem of adjoint polynomials of a kind of graphs ΦS((kn+1)σ,nσ)∪2kSσ,Furthermore,we obtain chromatically equivalence of its complements.

chromatic polynomial,adjoint polynomials,factorization,chromatically equivalent graph, structure characteristics

O157.5

A

1008-5513(2013)06-0551-08

10.3969/j.issn.1008-5513.2013.06.001

2013-10-08.

國(guó)家自然科學(xué)基金(11061026,11071151).

索南仁欠(1969-),博士生,教授,研究方向：計(jì)算數(shù)學(xué),代數(shù)組合論.

2010 MSC:05C78