The endomorphism monoids and automorphism groups of Cayley graphs of semigroups

被引：6

作者：

Khosravi, Behnam ^{[1
]}

机构：

[1] Inst Adv Studies Basic Sci, Dept Math, Zanjan 4513766731, Iran

来源：

SEMIGROUP FORUM | 2017年 / 95卷 / 01期

关键词：

Cayley graphs of semigroups; Vertex-transitive graphs; The automorphism groups of Cayley graphs of semigroups; The endomorphism monoids of Cayley graphs of semigroups; COMBINATORIAL PROPERTIES; DIGRAPHS;

D O I：

10.1007/s00233-017-9875-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we introduce the notions of color-permutable automorphisms and color-permutable vertex-transitive Cayley graphs of semigroups. As a main result, for a finite monoid S and a generating set C of S, we explicitly determine the color-permutable automorphism group of [Theorem 1.1]. Also for a monoid S and a generating set C of S, we explicitly determine the color-preserving automorphism group (endomorphism monoid) of [Proposition 2.3 and Corollary 2.4]. Then we use these results to characterize when is color-endomorphism vertex-transitive [Theorem 3.4].

引用

页码：179 / 191

页数：13

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