关于一类图的自同态谱的研究

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。

Study on Endomorphism Spectra Some Graphs

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 in3].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.