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RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION 被引量:1
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作者 许进 《Acta Mathematica Scientia》 SCIE CSCD 2004年第4期577-582,共6页
A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also ... A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials. 展开更多
关键词 Graph Theory chromatic polynomial vertex-deleting recursive formula
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Graph Description by the Chromatic Polynomials 被引量:1
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作者 MA Hai-cheng LIU Hui-min ZHANG Hai-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第1期46-52,共7页
By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class hi-cycle graph and a second class bicycle graph... By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class hi-cycle graph and a second class bicycle graph(the Theorem 2), respectively. 展开更多
关键词 mono-cycle graph bi-cycle graph chromatic polynomial chromatic equivalence
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On Chromatic Polynomials of Complements of All Wheels with Any Missing Consecutive Spokes * 被引量:2
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作者 郝荣霞 刘彦佩 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第4期579-585,共7页
In this paper, a new method has been used to calculate the chromatic polynomials of graphs. In particular, the chromatic polynomials of complements of all wheels with any missing consecutive spokes are given.
关键词 chromatic polynomial WHEELS complement.
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The Factorization of Adjoint Polynomials of E^G(i)-class Graphs and Chromatically Equivalence Analysis 被引量:15
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作者 ZHANG Bing-ru YANG Ji-ming 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期376-383,共8页
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp+(r-1)^G(i) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ... Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp+(r-1)^G(i) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of (r - 1)G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp+(r-1)^G(i)∪(r - 1)K1 (1 ≤i≤p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements. 展开更多
关键词 chromatic polynomial adjoint polynomials FACTORIZATION chromatically equivalent graph structure characteristics
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On Chromatic Polynomials of Some Kinds of Graphs 被引量:1
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作者 Rong-xiaHao Yan-peiLiu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第2期239-246,共8页
In this paper,a new method is used to calculate the chromatic polynomials of graphs.The chro-matic polynomials of the complements of a wheel and a fan are determined.Furthermore,the adjoint polynomialsof F_n with n ve... In this paper,a new method is used to calculate the chromatic polynomials of graphs.The chro-matic polynomials of the complements of a wheel and a fan are determined.Furthermore,the adjoint polynomialsof F_n with n vertices are obtained.This supports a conjecture put forward by R.Y.Liu et al. 展开更多
关键词 chromatic polynomial WHEELS FANS COMPONENT
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Chromatically Equivalent Graphs with P(G, λ) = (λ- λ_1)(λ-λ_2)λ ̄(n+1)
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作者 韩伯棠 《Journal of Beijing Institute of Technology》 EI CAS 1995年第2期122+115-122,共9页
The author finds out all of the graphs with the same chromatic polynomial and proves some relevant theorems and corollaries.
关键词 trees(mathematics) coloring (mathematics) polynomials/chromatic polynomials
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CLASSIFICATION OF COMPLETE 5-PARTITE GRAPHS AND CHROMATICITY OF 5-PARTITE GRAPHS WITH 5n VERTICES
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作者 ZhaoHaixing LiuRuying ZhangShenggui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期116-124,共9页
For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two 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 chromaticall... For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two 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 unique.For 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 G.In this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/4.By 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 G.Many new chromatically unique 5 partite graphs are obtained. 展开更多
关键词 chromatic polynomial χ closed chromatic uniqueness.
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On Chromatically Equivalence of a Class of Graphs
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作者 ZHANG Shu-min 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期308-311,共4页
A class of new graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven.
关键词 chromatic polynomial chromatically equivalent graphs ladder graphs
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An Approach to Chromaticity of K_4-homeomorphs
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作者 PENGYan-ling 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期253-261,共9页
We introduce a new method for studying the chromaticity of K4-homeomorphs,by which some new results are obtained.
关键词 K4-homeomorphs chromatic equivalence chromatic polynomial
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The Reconstruction of q-Trees
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作者 韩伯棠 《Journal of Beijing Institute of Technology》 EI CAS 1997年第1期1-8,共8页
Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new ve... Let q be a positive integer.The graphs,called the q-trees are defined by recursion:the smallest q-tree is the complete graph K_q with q vertices,and a q-tree with n+1 vertices where n≥q is obtained by adding a new vertex adjacent to each of q arbitrarily selected but mutually adjacent vertices of q-tree with n vertices.Obviously,1-trees are the graphs which are generally called trees.In this paper,it is proved that for any positive integer q,q-tree is reconstructible. 展开更多
关键词 trees (mathematics) reconstruction (mathematics) polynomialS chromatic polynomials
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Chromatic Uniqueness of Certain Complete Tripartite Graphs 被引量:6
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作者 G. C. LAU Y. H. PENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第5期919-926,共8页
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 com... 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. 展开更多
关键词 Complete tripartit graphs chromatic polynomial chromatic uniqueness
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A Note on Chromatic Uniqueness of Completely Tripartite Graphs 被引量:4
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作者 Ke Yi SU Xiang En CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2010年第2期233-240,共8页
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 guarantee... 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. 展开更多
关键词 complete tripartite graph chromatic polynomial chromatic uniqueness color partition.
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Chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted Ⅱ
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作者 Roslan Hasni Ameen Shaman Ameen +1 位作者 Yee-Hock Peng Hai-xing Zhao 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第1期35-42,共8页
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... 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. 展开更多
关键词 chromatic polynomial chromatically closed chromatic uniqueness
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On the Minimum Real Roots of the Adjoint Polynomials of Graphs
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作者 任海珍 刘儒英 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第4期987-993,共7页
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 f... 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. 展开更多
关键词 chromatic polynomial adjoint polynomial roots.
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