中文摘要：

设Pn和Cn是具有n个顶点的路和圈,Sn是n个顶点的的星图,nG表示n个图G的不相交并。Srp＋1^G表示把星Sr＋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Sδ＋1^G,δ=rp;设m是自然数,图P（2m＋1）＋（m＋1）δ^SG是表示把（m＋1）Sδ＋1^G的每个分支的r度顶点分别与P2m＋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∪Sδ＋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,λk=（2^kq-1）＋2^k-1 qδ,讨论了图簇Pλk^SG∪（k-1）K1和Pλk^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。

英文摘要：

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.