## 41 Citations

The commuting graph of the symmetric inverse semigroup

- Mathematics
- 2012

The commuting graph of a finite non-commutative semigroup S, denoted G(S), is a simple graph whose vertices are the non-central elements of S and two distinct vertices x, y are adjacent if xy = yx.…

On the commuting graphs of Brandt semigroups.

- Mathematics
- 2020

The commuting graph of a finite non-commutative semigroup S, denoted by \Delta(S), is the simple graph whose vertices are the non-central elements of S and two distinct vertices x; y are adjacent if…

On large arbitrary girth of a semigroup

- Mathematics
- 2018

This paper is about girth of commuting graph of semigroup. Le t Sbe a finite non-commutative semigroup, its commuting graph, denoted by G(S), is a simple graph (which has no loops and multiple edges)…

On large arbitrary left path within a semigroup

- Mathematics
- 2017

This paper is about the construction of semigroups $S$ from some given graph $G$. Let $S$ be a finite non-commutative semigroup, its commuting graph, denoted by $G(S)$, is a simple graph (which has…

Can connected commuting graphs of finite groups have arbitrarily large diameter?

- MathematicsGeometry, Structure and Randomness in Combinatorics
- 2014

A two-parameter family, of finite, non-abelian random groups, is presented and it is proposed that, for each fixed k, the commuting graph of Gm,k is almost surely connected and of diameter k and would provide a large family of counterexamples to the conjecture of Iranmanesh and Jafarzadeh that the com- muting graph of a finite group, if connected, must have a bounded diameter.

Directed graphs of inner translations of semigroups

- Mathematics
- 2017

A mapping $$\alpha :S\rightarrow S$$α:S→S is called a Cayley function if there exist an associative operation $$\mu :S\times S\rightarrow S$$μ:S×S→S and an element $$a\in S$$a∈S such that $$\alpha…

Centralizers in the Full Transformation Semigroup

- Mathematics
- 2013

For an arbitrary set X (finite or infinite), denote by T(X) the semigroup of full transformations on X. For α∈T(X), let C(α)={β∈T(X):αβ=βα} be the centralizer of α in T(X). The aim of this paper is…

Equality of various graphs on finite semigroups

- Mathematics
- 2020

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we…

## References

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On semisimple commutative semigroups

- Mathematics
- 1975

This paper presents an application of radical theory to the structure of commutative semigroups via their semilattice decomposition. Maximal group congruences and semisimplicity are characterized for…

Valuation-like maps and the congruence subgroup property

- Mathematics
- 2001

Abstract.Let D be a finite dimensional division algebra and N a subgroup of finite index in D×. A valuation-like map on N is a homomorphism ϕ:N?Γ from N to a (not necessarily abelian) linearly…

On maximal congruences and finite semisimple semigroups

- Mathematics
- 1966

A right congruence p of a semigroup S is called modular if there is an element e of S such that eapa for all a in S. The element e is called a left identity for p. A similar definition is made for…

Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

- Mathematics
- 2002

We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let D be a finite dimensional division algebra having center K and let N ⊆ D× be a…

Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section

- Mathematics
- 2004

Abstract For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T(X, ρ, R) consisting of all mappings a from X to X such that a…

The algebraic theory of semigroups

- Mathematics
- 1964

This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into…

The Commuting Graph of Minimal Nonsolvable Groups

- Mathematics
- 2001

The purpose of this paper is to prove that if G is a finite minimal nonsolvable group (i.e. G is not solvable but every proper quotient of G is solvable), then the commuting graph of G has diameter…

ON THE COMMUTING GRAPH ASSOCIATED WITH THE SYMMETRIC AND ALTERNATING GROUPS

- Mathematics
- 2008

The commuting graph of a group G, denoted by Γ(G), is a simple undirected graph whose vertices are all non-central elements of G and two distinct vertices x, y are adjacent if xy = yx. The commuting…