关于一类图的自同态谱的研究

Study on Endomorphism Spectra Some Graphs

对一个图而言,有各种不同的自同态。德国数学家Knauer于1990年在文献[1]中首次提出了自同态谱和自同态型的概念,目的是通过图的各种不同的自同态来研究图的代数结构。文献[2]运用自同态型对树进行了刻画,而文献[3]对直径为3围长为6的2-部图作了讨论,并得到了这类图的自同态型。本文将给出奇圈及其补图的自同态谱和自同态型。

There are different endomorphis-ms for a graph. Knauer in 1990 first defined the endomorphism spectrum and the endomorphism type of a graph to study the algebraic structure which is put on a graph by this various endomorphisms. He characterized trees using their endomorphism types in [3]. The endomorphism type of bipartite graphs with diameter three and girth six is given. In this paper, we consider odd cycles and the complements, and obtain their endomorphism spectra and endomorphism types.