Abstract: Assume Pn to be the path with n vertices and Ψ*(4,n) be the graph consisting of 2P3 and Pn by coinciding two vertices of degree 2P3 of with two vertices of degree 1 of Pn,respectively.S*δ(δ=rm+1) Use to denote the graph,consisting of rPm+1 by coinciding one vertex of degree 1 of each component of rPm+1.The graph,consisting of Pn and nS*δ by coinciding each vertex of Pn with the vertex of degree r of every component of nS*δ,respectively,was labelled as PS*nδ.The symbol Ψ*S*(4δ,nδ) was applied to address the graph obtained from Ψ*(4,n) and(n+4)S*δ by coinciding each vertex of Ψ*(4,n) with the vertex of degree r of every component of Ψ*(4,n),respectively.By adopting the properties of adjoint polynomials.We proved that the factorization theorem of adjoint polynomials of two kinds of graphs PS*nδ∪tS*δ and Ψ*S*(4δ,nδ)∪tS*δ(n=2tq-1).Furthermore,the structural characteristics of chromatically equivalent graphs of their complements were obtained.