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On chromatic polynomials of Some Kinds of Graphs

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Acta Mathematicae Applicatae Sinica 2004年第2期20卷 239-246页

作者： Rong-xiaHao Yan-peiLiu DepartmentofMathematics BeijingJiaotongUniversityBeijing100044China

In this paper,a new method is used to calculate the chromatic polynomials of *** chro-matic polynomials of the complements of a wheel and a fan are ***,the adjoint polynomialsof F_n with n vertices are *** supports a ... 详细信息

关键词： chromatic polynomial wheels fans component

chromatic Uniqueness of Certain Complete Tripartite Graphs

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Acta Mathematica Sinica,English Series 2011年第5期27卷 919-926页

作者： G. C. LAU Y. H. PENG Faculty of Computer & Mathematical Sciences Universiti Teknologi MARA (Segamat Campus) 85100 Segamat Johor Malaysia Department of Mathematics and Institute for Mathematical Research Universiti Putra Malaysia 43400 UPM Serdang Malaysia

Let P（G,A） be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P（H, λ） = P（G, λ） implies H is isomorphic to G. Liu et al. [Liu, R. Y., Zhao, H. X., Ye, C. F.： A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs. Discrete Math., 289, 175 179 （2004）], and Lau and Peng [Lau, G. C., Peng, Y. H.： chromatic uniqueness of certain complete t-partite graphs. Ars Comb., 92, 353-376 （2009）] show that K（p - k,p - i,p） for i = 0, 1 are chromatically unique if p ≥ k ＋ 2 ≥ 4. In this paper, we show that if 2 〈 i 〈 4, the complete tripartite graph K（p - k,p - i,p） is chromatically unique for integers k ≥ i and p 〉 k2/4 ＋ i ＋ 1.

关键词： Complete tripartit graphs chromatic polynomial chromatic uniqueness

chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted Ⅱ

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 35-42页

作者： Roslan Hasni Ameen Shaman Ameen Yee-Hock Peng Hai-xing Zhao School of Mathematical Sciences Universiti Sains Malaysia Department of Mathematics and Institute for Mathematical Research University Putra Malaysia Department of Mathematics Qinghai Normal University

Let P（G, λ） be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G N H, if P（G, λ） = P（H, λ）. We write [G] = {HIH - G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6rid＋1 vertices according to the number of 7-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 6-partite graphs with certain star or matching deleted are obtained.

关键词： chromatic polynomial chromatically closed chromatic uniqueness

CLASSIFICATION OF COMPLETE 5-PARTITE GRAPHS AND chromaticITY OF 5-PARTITE GRAPHS WITH 5n VERTICES

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Applied Mathematics(A Journal of Chinese Universities) 2004年第1期19卷 116-124页

作者： ZhaoHaixing LiuRuying ZhangShenggui QinghaiNormalUniv Xining810008China NorthwesternPolytechnicalUniv. Xi＇an710072China

For a graph G,P(G,λ)denotes the chromatic polynomial of *** graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromatically *** a complete 5 partite graph G with 5n vertices, define θ(G)=(α(G,6)-2 n+1 -2 n-1 + 5)/2 n-2 ,where α(G,6) denotes the number of 6 independent partition s of *** this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/*** using these results the chromaticity of 5 partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is inve stigated,where S is a set of edges of *** new chromatically unique 5 partite graphs are obtained.

关键词： chromatic polynomial χ closed chromatic uniqueness.

A Note on chromatic Uniqueness of Completely Tripartite Graphs

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Journal of Mathematical Research and Exposition 2010年第2期30卷 233-240页

作者： Ke Yi SU Xiang En CHEN College of Mathematics and Information Science Northwest Normal University Gansu 730070 P. R. China

Let P（G,λ） be the chromatic polynomial of a simple graph G. A graph G is chromatically unique if for any simple graph H, P（H,λ） = P（G,λ） implies that H is isomorphic to G. Many sufficient conditions guaranteeing that some certain complete tripartite graphs are chromatically unique were obtained by many scholars. Especially, in 2003, Zou Hui-wen showed that if n 〉 1/3m2 ＋ 3/1k2 ＋ 3/1mk＋ 1/3m-1/3k＋ 3/2√m2 ＋ k2 ＋ mk, where n,k and m are non-negative integers, then the complete tripartite graph K（n - m,n,n ＋ k） is chromatically unique （or simply χ–unique）. In this paper, we prove that for any non-negative integers n,m and k, where m ≥ 2 and k ≥ 0, if n ≥ 3/1m2 ＋ 3/1k2 ＋ 3/1mk ＋ 3/1m - 3/1k ＋ 43, then the complete tripartite graph K（n - m,n,n ＋ k） is χ–unique, which is an improvement on Zou Hui-wen’s result in the case m ≥ 2 and k ≥ 0. Furthermore, we present a related conjecture.

关键词： complete tripartite graph chromatic polynomial chromatic uniqueness color partition.

chromatic Uniqueness of K4-Homeomorphs with Girth 8

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Journal of Mathematical Research with Applications 2012年第3期32卷 269-280页

作者： Weina SHI 1 ,Yongliang PAN1,Yan ZHAO 2 1.Department of Mathematics,University of Science and Technology of China, Anhui 230026,P.R.China 2.Institute of Electronics Engineering,China Academy of Engineering Physics, Sichuan 621900,P.R.China Department of Mathematics University of Science and Technology of China Anhui 230026 Institute of Electronics Engineering China Academy of Engineering Physics Sichuan 621900

In this paper,we determine all graphs of K4-homeomorphs of girth 8 which are chromatically unique.

关键词： chromatic polynomial chromatically unique graph K4-homeomorph.

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图的伴随多项式的最小实根(英文)

Journal of Mathematical Research and Exposition 2008年第4期28卷 987-993页

作者：任海珍刘儒英 Department of Mathematics and Information Science Qinghai Normal University

In this paper, we are concerned with the minimum real root of the adjoint polynomial of the connected graph G with cut-vertex u, in which G - u contains paths, circles or Dn components. Here Dn is the graph obtained from K3 and path Pn-2 by identifying a vertex of K3 with an end-vertex of Pn-2. Some relevant ordering relations are obtained. This extends several previous results on the minimum roots of the adjoint polynomials of graphs.

关键词： chromatic polynomial adjoint polynomial roots.