Y^(*)_(2,2,λ)形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 tree of shape as Y^(*)_((2,2,λ)) and chromatically equivalence of their complements

作　　者：熊鹏飞 张秉儒 XIONG Pengfei;ZHANG Bingru(Qinghai Communications Technical College,Xining 810016,China;College of Math.and Statistics,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）》2021年第6期538-544,共7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P_(n)和C_(n)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rP_(m+2)的每个分支的一个1度点重迭后得到的图,E S^(*)(r+1)m+r表示把P_(m)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E Sδ,δ=(r+1)m+r;设n(≥3)是奇数,λ=n+2-1(n+1)δ,图P ESλ表示把2-1(n+1)E Sδ的每个分支的r+1度顶点分别与P n的下标为奇数的2-1(n+1)个顶点重迭后得到的图,Y^(*)_((2,2,2λ+1))表示把P ESλ的两个r+2度点分别与2P 3的两个2度点重迭后得到的图,运用图的伴随多项式的性质,讨论了图簇E Sδ∪rK 1、Y^(*)_((2,2,2λ+1))∪K 1和Y^(*)_((2,2,2λ+3+δ))∪E Sδ的伴随多项式的因式分解式,令n=2 k-1 q-1,λk=(2 kq-1)+2 k-1 qδ,讨论了图簇Y^(*)_((2,2,λk))∪K 1和Y^(*)_((2,2,λk))∪(k-1)K 1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 P_(n) be a path with n vertices and let C_(n) be a cycle with n vertices,and nG be the union of n graphs G without common vertex.We denote by S^(*)_(r(m+1)+1) the graph consisting of rP_(m+2) and by coinciding r vertices of degree 1 of rP_(m+2),Let E S^(*)_((r+1)m+r) be the graph consisting of P_(m) and S^(*)_(r(m+1)+1) by coinciding a vertex of degree 1 of P_(m) with the vertex of degree r of S^(*)_(r(m+1)+1),can be abbreviated to E Sδ,δ=(r+1)m+r;let n(≥3)is an odd number,λ=n+2-1(n+1)δ,Let P ESλbe the graph consisting of 2-1(n+1)E Sδand P n by coinciding the vertex of degree r+1 of every component of 2-1(n+1)E Sδwith 2-1(n+1)vertices which subscript be odd of P n,respectively;Let Y^(*)(2,2,2λ+1)be the graph consisting of P ESλand 2 P 3 by coinciding two vertices of degree r+2 of P ESλwith two vertices of degree 2 of 2 P 3,respectively;By unsing the properties of adjoint polynomials of graphs or even,We discuss the factorizations of adjoint polynomials of graphs E Sδ∪rK 1 and Y^(*)_((2,2,2λ+1))∪K 1 and Y^(*)_((2,2,2λ+3+δ))∪E Sδ,Let n=2 k-1 q-1 andλk=(2 kq-1)+2 k-1 qδ,We discuss the factorizations of adjoint polynomials of graphs Y^(*)_((2,2,λk))∪K 1 and Y^(*)_((2,2,λk))∪(k-1)K 1,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]