P_λ^(SG)形图的伴随多项式的分解及其补图的色等价性  

Factorizations of adjoint polynomials of graphs of shape as PSGλand chromatically equivalence of their complements

作　　者：熊鹏飞 张秉儒[2] XIONG Pengfei ZHANG Bingru(Qinghai Traffic Vocational Technical College 810016 ,China Department of Mathemetics,Qinghai Normal University,Xining 810008,China)

机构地区：[1]青海交通职业技术学院,青海西宁810016 [2]青海师范大学数学系,青海西宁810008

出　　处：《南昌大学学报（理科版）》2017年第2期108-113,共6页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10861009;10761008);青海省自然科学基金资助项目(2011-Z-911)

摘　　要：设P_n和C_n是具有n个顶点的路和圈,S_n是n个顶点的的星图,nG表示n个图G的不相交并。S_(rp+1)~G表示把星S_(r+1)的r个1度点分别与rG的每个分支的第i个顶点重迭后得到的图,可简记为S_(δ+1)~G,δ=rp;设m是自然数,图P_((2 m+1)+(m+1)δ)~SG是表示把(m+1)S_(δ+1)~G的每个分支的r度顶点分别与P_(2m+1)的下标为奇数的m+1个顶点重迭后得到的图,运用图的伴随多项式的性质,讨论了图簇PP_((2 m+1)+(m+1)δ)~SG∪K1(m为奇数)和P_((2 m+1)+(m+1)δ)~SG∪S_(δ+1)~G(m为偶数)的伴随多项式的因式分解式,令m=2^(k-1) q-1,λ_k=(2~kq-1)+2^(k-1)qδ,讨论了图簇P_λk^(SG)∪(k-1)K_1和P_λk^(SG)的伴随多项式的因式分解式,进而证明了这些图的补图的色等价性。Let Pnbe a path with nvertices,Cn be a cycle with n vertices,Sn be a star with n vertices,and nG be the union of ngraphs G without common vertex.It denoted by Srp＋1^G the graph consisting of Sr＋1 and rG by coinciding r vertices of degree 1 of S（rp＋1） with the ith vertex of every component of rG,respectively,abbreviated as Sδ＋1^G,δ=rp;Let m be a nature number,P（2 m＋1）＋（m＋1）^SG δbe the graph consisting of（m＋1）Sδ＋1^G and P（2m＋1） by coinciding the vertex of degree r of every component of （m＋1）Sδ＋1^G with m＋1vertices whose subscripts are odd of P2 m＋1,respectively.By using the properties of adjoint polynomials of graphs,it discussed the factorizations of adjoint polynomials of graphs P（2 m＋1）＋（m＋1）δ^SG ∪ K1（where m is odd）and P（2 m＋1）＋（m＋1）δ^SG∪Sδ＋1^G（where m is even）.Letting m=2^kq-1andλn=（2^nq-1）＋2^n-1qδ,it discussed the factorizations of adjoint polynomials of graphs Pλk^SG∪（k-1）K1 and Pλk^SG.Furthermore,it proved the chromatic equivalence of complements of these graphs.

关 键 词：伴随多项式 因式分解 色等价性 

分 类 号：O157.5[理学—数学]