图的伴随多项式整除性质的研究

Divisible Properties of Adjoint Polynomial of Special Graphs

用P_n和C_n分别表示具有n个顶点的路和圈,h(P_n,x)和h(C_n,x)依次表示它们的伴随多项式。本文证明了当m≥4时,h(P_n,x)和h(C_n,x)分别能够被h(C_m,x)整除的充要条件。

Let Pn denote the path with n vertices and Cn denote the cycle with n vertices, Let h(Pn,x) and h(Cn,x) denote adjoint polynomial of Pn and Cn in thier given order. In this paper, I proved that following Theorems; If m≥4, h(Cn,x) is divisible by h(Cm,x) if and only if n = mt, h (Pn,x) is divisible by h(Cm,x) if and only if n = ms-1. where t is any positive odd integer and s is any positive even integer.