一类Y^(SG)(γλ,n)∪βS_n^G形图簇的伴随分解及其补图的色等价性  

The Factorization of Adjoint Polynomials of Graphs Y^(SG)(γλ,n)∪βS_n^G and Chromatically Equivalence of Their Complements

作　　者：郝萃菊[1] 

机构地区：[1]青海大学成教学院,青海西宁810006

出　　处：《数学的实践与认识》2014年第4期241-250,共10页Mathematics in Practice and Theory

摘　　要：设G是m阶连同图,我们用S_n^G(n=km+1)表示把kG的每个分支的d_i度点分别与星图S_k+1的k个1度点重迭后得到的图,Y^(SG)(r_1n,n)表示把r_1S_n^G中每个分支的k度点依次与图的k度点邻接后得到的图,Y^(SG)(r_2λ_1,n)表示把τ_2Y^(SG)(τ_1n,n)中每个分支的r_1+k度点依次与图S_n^G的k度点邻接后得到的图,若k≥3,用Y^(sG)(r_kλ__(k-1),n)表示把τ_kY^(sG)(r_(k-1)λ_(k-2),n)中每个分支的τ_(k-1)+k度顶点依次与图S_n^G的k度点邻接后得到的图,这里λ_k=r_kλ_(k-1)+n.运用图的伴随多项式的性质,证明了一类新的图簇Y^(sG)(r_kλ__(k-1),n)∪β_kS_n^G的伴随多项式的因式分解定理,进而得到了这类图的补图的色等价图.Let G be a connected graph with m vertices and let SGn （n =km ＋ 1） be the graph consisting of kG and Sk＋1 by coinciding a vertex of degree diof each component of kG with k vertices of degree 1 of Sk＋1.We denote by YSG （r1n,n） the graph consisting of （r1 ＋ 1）SGn by adjacenting the vertex of degree k of every component of r1SGn with the vertex of degree k of SGn,respectively,and let YSG （r2λ1,n） be the graph obtained from r2YSG （r1n,n）and SGn by adjacenting the vertex of degree r1 ＋ k of every component of r2YSG （r1n,n）with the vertex of degree k of SGn,respectively,If k ≥ 3,YSG （rkλk-1,n） be the graph consisting of rkYSG （rk-1λk-2,n） and SGn by adjacenting the vertex of degree rk-1 ＋ k of every component of rkYSG （rk-1λk-2,n） with the vertex of degree k of SGn,respectively,where λk =rkλk-1 ＋ n,By applying the properties of adjoint polynomials,We prove that factorization theorem of adjoint polynomials of a kind of new graphs YSG （rkλk-1,n）UβkSGn,Furthermore,We obtain structure characteristics of chromatically equivalent graphs of their complements.

关 键 词：色多项式 伴随多项式 因式分解 色等价 

分 类 号：O157.5[理学—数学]