中文摘要：

设Pn和Cn分别是n个顶点的路和圈,用Sk＊n＋1表示把kPn＋1的每个分支的一个1度点重迭在一起得到的图,ωδ（δ=rm＋1）表示把rCm＋1中每个分支的一个1度点重迭后得到的图,并用Vω（kn＋1）δ表示把图Sk＊n＋1的kn＋1个顶点与（kn＋1）ωδ的每一个分支的2r度点依次重迭后得到的图。运用图的伴随多项式的性质,证明了Vωxδ∪yωδ（x,y∈N）形图簇的伴随多项式的因式分解定理,进而证明了这类图簇的补图的色等价性。

英文摘要：

Let Pn be the path with n vectices and let Cn be the cycle with n vectices,and let S＊kn＋1 be the graph consisting of kPn＋1 by coinciding the vertex of degree 1 of each component of kPn＋1 respectively;and let ωδ be the graph consisting of rCm＋1 by coinciding one vertiex of degree 2 of each component of rCm＋1.respectively;and let Vω（kn＋1）δ be the graph obtained from S＊kn＋1 and（kn＋1）ωδ by coinciding each vertex of S＊kn＋1 with the vertex of degree 2r of every component of,respectively.Applying the properties of adjoint polynomials,we prove that factorization theorem of adjoint polynomials of theVωxδ∪yωδ（x,y∈N）-shaped graphs,where δ=rm＋1 and x,y∈N.Furthermore,we obtain the structure characteristics of chromatically equivalent graphs of their complements.