图K_n-E(k_0P_3(∪ri=1k_iP(q_i-1)))的色唯一性

CHROMATIC UNIQUENESS OF K n Ek 0P 3(∪ri=1k iP q i-1 )

记δｎ＝ｋ≤ｎｋｎ－ｋ，在本文中证明了：ｒ∈Ｎ，若ｉ∈｛１，２，…，ｒ｝，ｑｉ（＞５）都是素数，并且［（δｑｉ－１－１）！＋１］／δｑｉ－１是正整数，则图簇Ｋｎ－Ｅｋ０Ｐ３∪ｋ１Ｐｑ１－１∪ｋ２Ｐｑ２－１∪…∪ｋｒＰｑｒ－１是色唯一的。

Let P n denote the path with n vertices and h(P n,x) denote the Adjoint polynomial of P n . Let δ n =h(P n,1)=k≤n k n k.  In this paper, I prove P n is irreducible path n=3 or n=q-1 , where q(≥3) is a prime and [(δ q-1 -1)!+1]/δ q-1  is a integer number, and graphs K n Ek 0P 3(∪ri=1k iP q i 1 ) which satisfied some condition is chromatically unique. I improve the results obtained by Lin Ruying and Li Nianzu in .