We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On transitive Cayley graphs of homogeneous inverse semigroups.
- Authors
Ilić-Georgijević, E.
- Abstract
Let S be a pseudo-unitary homogeneous (graded) inverse semigroup with zero 0, that is, an inverse semigroup with zero, and with a family { S δ } δ ∈ Δ of nonzero subsets of S, called components of S, indexed by a partial groupoid Δ , that is, by a set with a partial binary operation, such that S = ⋃ δ ∈ Δ S δ , and: i) S ξ ∩ S η ⊆ { 0 } for all distinct ξ , η ∈ Δ ; ii) S ξ S η ⊆ S ξ η whenever ξ η is defined; iii) S ξ S η ⊈ { 0 } if and only if the product ξ η is defined; iv) for every idempotent element ϵ ∈ Δ , the subsemigroup S ϵ is with identity 1 ϵ ; v) for every x ∈ S there exist idempotent elements ξ , η ∈ Δ such that 1 ξ x = x = x 1 η ; vi) 1 ξ 1 η = 1 ξ η whenever ξ η ∈ Δ is an idempotent element, where ξ , η are idempotent elements of Δ . Let A be a subset of the union of the subsemigroup components of S, which does not contain 0. By Cay (S ∗ , A) we denote a graph obtained from the Cayley graph Cay (S , A) by removing 0 and its incident edges. We characterize vertex-transitivity of Cay (S ∗ , A) and relate it to the vertex-transitivity of its subgraph whose vertex set is S μ \ { 0 } , where μ is the maximum element of the set of all idempotent elements of Δ , with respect to the natural order.
- Subjects
CAYLEY graphs; IDEMPOTENTS; BINARY operations
- Publication
Acta Mathematica Hungarica, 2023, Vol 171, Issue 1, p183
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-023-01375-x