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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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The Roots of Adjoint Polynomial of the Graphs Contain Triangles 被引量:3
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作者 YECheng-fu 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期280-285,共6页
We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root ... We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple. 展开更多
关键词 ROOT adjoint polynomial
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The Relation on the Coefficients and Roots of Adjoint Polynomial and Its Application
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作者 冶成福 王波 刘儒英 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第3期317-324,共8页
The parameter R(G) is the function about the front three coeffcients of the adjoint polynomial of graph G. In the paper, the range of R(G) is given when β(G) 〈 β(Dn), where β(G) is the minimum root of th... The parameter R(G) is the function about the front three coeffcients of the adjoint polynomial of graph G. In the paper, the range of R(G) is given when β(G) 〈 β(Dn), where β(G) is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tDn is completely depicted.Furthermore, a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained. 展开更多
关键词 chromatically equivalent adjoint polynomial the least root
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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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THE ROOTS OF σ-POLYNOMIALS 被引量:2
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作者 ZhaoHaixing LiuRuying LiXueliang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第2期230-234,共5页
Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G,where δ(G)=|E(G)||V(G)|2. If σ(G,x) has at least an unreal root,then G is said to be a σ-unreal gr... Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G,where δ(G)=|E(G)||V(G)|2. If σ(G,x) has at least an unreal root,then G is said to be a σ-unreal graph.Let δ(n) be the minimum edge-density over all n vertices graphs with σ-unreal roots. In this paper,by using the theory of adjoint polynomials, a negative answer to a problem posed by Brenti et al. is given and the following results are obtained:For any positive integer a and rational number 0≤c≤1,there exists at least a graph sequence {G i} 1≤i≤a such that G i is σ-unreal and δ(G i)→c as n→∞ for all 1≤i≤a,and moreover, δ(n)→0 as n→∞. 展开更多
关键词 ROOTS σ-polynomial adjoint polynomial.
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Chromatic Uniqueness of the Complement of T_m(l, 4, m - 6)
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作者 ZHANGShu-min 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期133-141,共9页
In the paper, we prove that the complement of Tm(1,4,m-6)(m> 10) is chromatically unique if and only if m≠5k(k≥2).
关键词 the least root adjoint polynomial chromatic uniqueness
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