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数学进展
研究论文
两类图簇的伴随多项式的因式分解及色性
The Factorzation of Adjoint Polynomials of Two Kinds of Graphs and Chromatically Equivalence Analysis

张秉儒
ZHANG Bing-ru

青海师范大学数学系 西宁,青海, 810008
(Department of Mathematics, Qinghai Normal University, Xining, Qinghai, 810008, P. R. China

收稿日期: 2004-02-25
出版日期: 2004-02-25

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摘要 令Sk+1表示k+1阶星图,ψ*(2k,n)表示2Sk+1的两个k度点分别与路Pn的两个1度点重迭后得到的图.对于1≤i≤2k+n=q,用Srq+1*(i)表示rψ*(2k,n)的每个分支的第i个顶点依次与Sr+1的r个1度点重迭后得到的新图;Γpq+1*(i)表示pψ*(2k,n)的每个分支的第i个顶点及其对称点依次与S2p+1的2p个1度点配对且重迭后得到的新图.我们通过研究这两类新图与一定数目的孤立点组成的并图的伴随多项式的因式分解,证明了上述并图的补图的色等价图的结构定理.
关键词 色多项式伴随多项式因式分解色等价性非色唯一图    
Abstract:Let Sk+1 be the star of order k + 1, and let ψ*(2k, n) be the graph consisting of 2Sk+1 and Pn by coinciding two vertices of degree k of 2Sk+1 with two vertices of degree 1 of Pn, respectively. For 1 ≤ i ≤2k + n = q, we denote by Srq+1 *(i) the new graph consisting of rψ (2k, n) and Sr+i by coinciding the ith vertex of everyone of rψ (2k, n) with r vertices of degree 1 of Sr+1, respectively; and let Γpq+1 *(i) denote the new graph obtained from pψ(2k, n) and S2p+1 by match-coinciding the ith vertex and its symmetric vertex Vq-i+1 of each component of pψ*(2k, n) with 2p vertices of degree 1 of S2p+1, respectively. By studying factorization of adjoint polynomials of the union consisting of these new graphs and some isolated vertices, we prove that structure theorem of the chromatically equivalent graphs of their complements.
Key words adjoint polynomial    factorization    chromatic equiva- lence    chromatic non-uniqueness graph.
[1] 杨利民;王天明;. 色多项式的显示公式[J]. 数学进展, 2006, 35(1): 55-66.
[2] 张秉儒. S~G类图簇的伴随多项式的因式分解及色性分析[J]. 数学进展, 2004, 33(4): 425-433.
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