关于图多项式的一个问题

ON A PROBLEM OF POLYNOMIALS ON GRAPH

本文利用图的邻接矩阵的最小多项式,定出了两类只有平凡的多项式图的图。为解答文献[3]提出的一个问题,给出了两个充分条件。

Let G be a simple graph with adjacency matrix A, and p (x) is a polynomial with rational coefficients. When a polynomial in the adjacency matrix of a graph will yield the adjacency matrix of another graph? This remains an unsolved problem. In this paper, we give a partial solution to the question of [3].