| 图的伴随多项式的两个因式分解定理及其应用 |
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| 引用本文： | 张秉儒.图的伴随多项式的两个因式分解定理及其应用[J].数学研究与评论,2003,23(2):355-361. |
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| 作者姓名： | 张秉儒 |
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| 作者单位： | 青海师范大学数学系,青海,西宁,810008 |
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| 基金项目： | 国家自然科学基金资助项目(10061003). |
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| 摘 要： | 设G是m阶连通图,Pm是m个顶点的路.令Skm+1G(i)表示把kG的每一个分支的第i(1≤i≤m)个顶点依次与星图Sk+1的k个1度顶点重迭后得到的图;令Gi1S*(q,km)表示q阶图G的顶点Vi1与Skm+1p(1)的k度顶点重迭后得到的图
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| 关 键 词： | 色多项式 伴随多顶式 因式分解 色等价性 色唯一性 |
| 文章编号： | 1000-341X(2003)02-0355-07 |
| 收稿时间： | 2000/12/4 0:00:00 |
| 修稿时间： | 2000年12月4日 |
Two Factorization Theorems of Adjoint Polynomials of Graphs with Application |
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| ZHANG Bing-ru.Two Factorization Theorems of Adjoint Polynomials of Graphs with Application[J].Journal of Mathematical Research and Exposition,2003,23(2):355-361. |
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| Authors: | ZHANG Bing-ru |
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| Institution: | Dept. of Math.; Qinghai Normal University; Xining; China |
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| Abstract: | Let G be a connected graph of order p and Pm be a path with m vertices. Let S_(km+1)~G(i) denote the graph consisting of rG and the star Sk+1 by coinciding the z'th vertex of everyone of
rG with k-1 vertices of degree 1 of Sk+1 ; let Gf (q,km) denote the graph obtained from a graph G of order 1 and S_(km+1)~p(1) by coinciding the vertex vil of G with the vertex of degree k of S_(km+1)~p(1). We give and prove that factorization theory of adjoint polynomials of graphs S_(km+1)~G(i) U (k-1)K1 and G_i1~s (q,km) , and we obtain some structure characteristics of the chromatically equivalent graphs of their complements. |
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| Keywords: | chromatic polynomial adjoint polynomial factorization chromatically equivalence chromatically uniqueness |
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