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- Title
On Cayley graphs of semilattices of semigroups.
- Authors
Khosravi, Behnam; Khosravi, Bahman
- Abstract
The Cayley graphs of some semigroups have been considered by many authors. Let S=⋃ S be a semilattice of semigroups and C⊆ S. In this note, we investigate the color automorphism vertex-transitivity of the Cayley graph Cay( S, C), and as one of our main results, we show that under a natural assumption on this graph, the behavior of the Cayley graph Cay( S, C) is essentially related to the properties of the Cayley graph Cay( Y, D), where D={ a∈ Y|∃ c∈ C: c∈ S}. Because of this relation, first we study the Cayley graph Cay( T, D), where T is a semilattice and D⊆ T, and we give some useful descriptions for semilattice graphs. Then we use these results to characterize the color automorphism vertex-transitive Cayley graphs of semilattices of semigroups under our assumption.
- Subjects
CAYLEY graphs; SEMILATTICES; SEMIGROUPS (Algebra); AUTOMORPHISM groups; GRAPH theory; NUMERICAL analysis; MATHEMATICAL analysis
- Publication
Semigroup Forum, 2013, Vol 86, Issue 1, p114
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-012-9384-4