一类树的伴随多项式的分解及其补图的色等价性  

The factorizations of adjoint polynomials of a kinds of tree and chromatically equivalence of their complements

作　　者：熊鹏飞 张秉儒 XONG Pengfei;ZHANG Bingru(Qinghai Communications Technical College,Xining Qinghai 810016,China;College of Math.And statistics,Qinghai Normal University,Xining Qinghai 810008,China)

机构地区：[1]青海交通职业技术学院,青海西宁810006 [2]青海师范大学数学与统计学院,青海西宁810008

出　　处：《南昌大学学报（理科版）》2020年第5期412-416,共5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项目(2011-Z-911)。

摘　　要：设Pn和Cn是具有n个顶点的路和圈,nG表示n个图G的不相交并。令S*r(m+1)+1表示rPm+2的每个分支的一个1度点重迭后得到的图,ES*(r+1)m+r表示把Pm的一个1度点与S*r(m+1)+1的r度点重迭后得到的图,可简记为ESδ,δ=(r+1)m+r;设n(≥4)是偶数,λ=(n+1)+2-1(n+2)δ,令图PESλ是表示把2-1(n+2)ESδ的每个分支的r+1度顶点分别与Pn+1的下标为奇数的2-1(n+2)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ESδ∪rK1、PES2λ-1-δ∪ESδ和PES2λ-1-δ∪2ESδ∪rK1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 Pn be a path with n vertices,Cn a cycle with n vertices,and nG the union of n graphs G without common vertex.We denote by S*r(m+1)+1 the graph consisting of rPm+2 obtained by coinciding r vertices of degree 1 of rPm+2.Let ES*(r+1)m+r be the graph consisting of Pm and S*r(m+1)+1 by coinciding a vertex of degree 1 of with the vertex of degree of,abbreviated as,.Let be an even number,and,be the graph consisting of ESδ,δ=(r+1)m+r;let n(≥4)and by coinciding the vertex of degreeλ=(n+1)+2-1(n+2)δ,PESλof r+1 every component of 2-1(n+2)ESδand Pn+1 with 2-1(n+2)ESδwith 2-1(n+2)vertices which subscript be odd of Pn+1,respectively.By using the properties of adjoint polynomials of graphs,we discuss the factorizations of adjoint polynomials of graphs ESδ∪rK1 and PES2λ+1∪ESδand PES2λ-1-δ∪2ESδ∪rK1.Furthermore,we prove chromatically 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]