【摘要】 令S1,k表示k+1个顶点的星,Pm表示m个顶点的路,G是任意的p阶连通图.设V(Pm)={V1,V2,…,Vm-1,Vm}及相应的度序列为(1,2,…,2,1)。SkPm(i+)1表示把kPm的每个分支的第i个顶点Vi分别与星S1,k的k个1度点重迭后得到的图,用GjS1*j2(…i)jt(p,tkm)表示把tSPkm(i+)1的每个分支的k度点分别与图G的顶点uj1,uj2,…,ujt(t≤p)重迭后得到的图,这里p≥1,k≥2,m≥3,1≤i≤m,t≥1.我们通过讨论图簇SkPm(i+)1∪(k-1)K1、S2Pr(mi)+1,SP((2ri)-1)m+1以及GSj1*j2(…i)jt(p,2rmt),GSj1*j2(…ij)t(p,(2r-1)mt)的伴随多项式的因式分解,证明了它们的补图的色等价图的结构定理.推广了张秉儒证明的文[8]中的定理2和定理4。更多还原

【Abstract】 Let S_1,k be the star with k+1 vertices,and let P_m denote the path with m vertices,let G be an arbitary connected graph.And let V（P_m）={V₁,V₂,…V_m-1,V_m} with corresponding degree sequence（1,2,…,2,1）.Denote by S^p（i）_km+1 the graph consisting of kP_m and S_1,k by coinciding the ith vertex of each component of kP_m with k vertices of degree 1 of S_1,k respectively.Let G^s*（i）_j1j2…jt（p,tkm） denote the graph obtained from tS^p（i）_km+1 and G by coinciding the vertex of degree k of everyone of tS^p（i）_km+1 with vertices u_j1,u_j2,…,u_jt（t≤p） of graph G respectively,where p≥1,k≥2,m≥3,1≤i≤m,t≥1.By studyying the factorization of adjoint polynomials of the graphs S^p（i）_km+1∪（k-1）K₁,S^p（i）_2rm+1,S^p（i）_{（2r-1）m+1},G^s*（i）_j1j2…jt（p,2rmt） and G^s*（i）_j1j2…jt（p,（2r-1）mt）,the paper proved the structure theorem of the chromatically equivatent graphs of their complements,and improve Theorem 2 and Theorem 4 in Zhang Bing-ru\.更多还原