Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2509.15656

On the structure and skeletals of principal ideal graphs of inverse semigroups

C S Preenu·R S Indu·Sijo George
View original source ↗Read source document ↗Export metadata ↓

Abstract

The principal left ideal graph of a semigroup is a simple graph whose vertices are the non-zero elements of the semigroup, and two vertices are adjacent if their principal left ideals intersect non-trivially. In this paper, we study the structure of the principal ideal graphs of inverse semigroups, particularly symmetric inverse semigroups. We also introduce the concept of skeletal of a graph and show that the principal ideal graph of an inverse semigroup has a skeletal, which is a simple graph with vertex set as $\mathcal{L}$ classes of non-zero elements. It is also proved that the principal ideal graph of symmetric inverse semigroups has a skeletal which is isomorphic to the intersection graph on the power set of a non-empty set.

Explore related subjects

math.GRmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C S Preenu, R S Indu, Sijo George. 2025-09-19. On the structure and skeletals of principal ideal graphs of inverse semigroups. https://arxiv.org/abs/2509.15656

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reversibility and its asymptotic counting in Picard group

We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.

math.GR↗
arXiv2026

Conjugator length in finitely generated groups

We describe all functions $\mathbb{N}\rightarrow \mathbb{N}$ that can be realized, up to the standard equivalence, as conjugator length functions of finitely generated groups. Furthermore, we show that any two increasing functions $f,g\colon \mathbb N\to \mathbb N$ can be simultaneously realized as conjugator length functions of finitely generated, commensurable (in particular, quasi-isometric) groups.

math.GR↗
arXiv2026

The spectrum of conjugator length functions

A recent program tries to find which functions appear as conjugator length functions. In this note, we show that any (computable) increasing function larger than $n$ appears as $\mathrm{Cl}_G$ for some finitely generated (recursively presented) group. On the other hand, we demonstrate that either $\mathrm{Cl}_G$ must be constant or $\mathrm{Cl}_G(n)\succ n$. Combining these, we obtain a complete description of which functions appear as conjugator length functions of finitely generated groups.

math.GR↗