图的伴随多项式的两个因式分解定理及其应用  

Two Factorization Theorems of Adjoint Polynomials of Graphs with Application

作　　者：张秉儒[1] 

机构地区：[1]青海师范大学数学系,青海西宁810008

出　　处：《Journal of Mathematical Research and Exposition》2003年第2期355-361,共7页数学研究与评论（英文版）

基　　金：国家自然科学基金资助项目(10061003).

摘　　要：设G是m阶连通图,Pm是m个顶点的路.令S_(km+1)~G(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G_i1^(S)(q,km)表示q阶图G的顶点Vi1与S_(km+1)~p(1)的k度顶点重迭后得到的图.我们给出并证明了图S_(km+1)~G(i)∪(k-1)K1与G_i1^(S)(q,km)的伴随多项式的因式分解定理,并且得到了它们的补图的色等价图的结构性质.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.

关 键 词：简单图 伴随多项式 因式分解定理 挖顶补点法 断路补圈法 色多项式 理想子图 连通图 

分 类 号：O157.5[理学—数学] O174.14[理学—基础数学]