p^2阶非正规Cayley图的核

Cores of Non-normal Cayley Graphs of Order p^2

图的核的研究是当前图论特别是代数图论中的一个前沿课题.一个图的核定义为与该图同态等价的最小阶的图.本文通过讨论p^2阶(p是素数)非正规Cayley图是否存在与其同态等价的诱导子图,研究该Cayley图与其诱导子图的色数、团数和独立数之间的关系,进而确定两个图之间是否存在同态等价.在此基础上确定出p^2阶非正规Cayley图的核.

The study of the cores of different types of graphs is a relatively new and active topic in graph theory, especially in algebraic graph theory. The core of a graph is defined to be a graph of smallest order which is homomorphically equivalent to the original graph. In this paper, we study the cores of non-normal Cayley graphs of order p2, where p is a prime. Our study is mainly based on investigating the relationship between the chromatic number, clique number and independence number of the graph and its induced subgraph. We then determine whether there is an induced subgraph which is homomorphically equivalent to the given graph.Based on this, we determine the cores of all non-normal Cayley Graphs of order p^2.