另一类Pλ^ES形图伴随多项式的分解及其补图的色等价性  

The factorizations of adjoint polynomials of another graphs of shape as Pλ^ES and chromatically equivalence of their complements

作　　者：熊鹏飞 张秉儒 XIONG Peng-fei;ZHANG Bing-ru(Department of Basic,Qinghai Communications Technical College,Xining Qinghai 810016,China;School of Mathematics and Statistics,Qinghai Normal University,Xining Qinghai 810008,China)

机构地区：[1]青海交通职业技术学院基础部,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：《青海师范大学学报（自然科学版）》2020年第4期8-15,共8页Journal of Qinghai Normal University(Natural Science Edition)

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：假设Pn和Cn是存在n个顶点的路和圈,nG表示n个图G的不相交并。令Sr(m+1)+1*表示rPm+2的各个分支的一个1度点重迭后获得的图,E(r+1)m+rS*表示将Pm的1度点与Sr(m+1)+1*的r度点重迭之后得到的结果,可将其记作EδS,δ=(r+1)m+r;假设n(≥4)为偶数,λ=(n+1)+2-1(n+2)δ,令PλES是将2-1(n+2)EδS的各分支的r+1度顶点先后与Pn+1的下标为奇数的2-1(n+2)个顶点重迭后获得的结果,对图的伴随多项式进行应用,讨论了图簇EδS∪rK1、P2λ+1ES∪K1和P2λ+1ES∪EδS因式分解式,假定n=2k-1q-2,λk=(2kq-1)+2k-1qδ,研究图簇PλkES∪(k-1)K1和PλkES对应的因式分解式,从而检验这部分图的补图的色等价性。Let Pn be a path with n vertices and letCn be a cycle with n vertices,and nG be the union of n graphs Gwithout common vertex.We denote by Sr(m+1)+1* the graph consisting of rPm+2 and by coinciding r vertices of degree 1 of rPm+2,Let E(r+1)m+rS* be the graph consisting of Pm and Sr((m+1)+1)* by coinciding a vertex of degree 1 of Pm with the vertex of degree r of Sr(m+1)+1*,can be abbreviated to EδS,δ = (r+1)m +r;let n(≥4)is an even number,andλ= (n +1)+2-1(n+2)δ, PλES be the graph consisting of 2-1(n+2)EδS and Pn+1 by coinciding the vertex of degree r+1 of every component of 2-1(n+2)EδS with 2-1(n+2) vertices which subscript be odd of Pn+1,respectively;By unsing the properties of adjoint polynomials of graphs or even,We discuss the factorizations of adjoint polynomials of graphs EδS ∪rK1 and P2λ+1ES ∪ K1 and P2λ+1ES∪EδS,Letn=2k-1q-2,and λk =(2kq-1)+2k-1 qδ,We discuss the factorizations of adjoint polynomials of graphs PλkES∪(k-1)K1 and PλkES,further,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]