Corpus ID: 236318376

The cyclic graph of a semigroup

  title={The cyclic graph of a semigroup},
  author={Sandeep Dalal and Jitender Kumar and Siddharth Singh},
The cyclic graph Γ(S) of a semigroup S is the simple graph whose vertex set is S and two vertices x, y are adjacent if the subsemigroup generated by x and y is monogenic. In this paper, we classify the semigroup S such that whose cyclic graph Γ(S) is complete, bipartite, tree, regular and a null graph, respectively. Further, we determine the clique number of Γ(S) for an arbitrary semigroup S. We obtain the independence number of Γ(S) if S is a finite monogenic semigroup. At the final part of… Expand


Chromatic Number of the Cyclic Graph of Infinite Semigroup
The purpose of this note is to prove that the chromatic number of Γ ( S) is at most countable. Expand
Coloring the Power Graph of a Semigroup
  • Y. Shitov
  • Mathematics, Computer Science
  • Graphs Comb.
  • 2017
It is shown that the chromatic number of P(G) is at most countable, answering a recent question of Aalipour et al. Expand
On the Structure of the Power Graph and the Enhanced Power Graph of a Group
It is proved that for every group G, the clique number of the power graph of $G$ is at most countably infinite and the graph is called theenhanced power graph. Expand
A matrix ring with commuting graph of maximal diameter
  • Y. Shitov
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2016
This work provides an example of a field F and an integer n such that the commuting graph of Mat n ( F ) has maximal possible diameter, equal to six. Expand
On cyclic graphs of finite semigroups
In this paper, we define and study the cyclic graph ΓS of a finite semigroup S. We obtain some graph theoretical properties of ΓS including its dominating number, independence number and genus of theExpand
The Cyclic Graph of a Finite Group
The cyclic graph of a finite group is as follows: take as the vertices of and join two distinct vertices and if is cyclic. In this paper, we investigate how the graph theoretical properties ofExpand
A Characterization of Cayley Graphs of Brandt Semigroups
In this paper, first we characterize Cayley graphs of finite Brandt semigroups, and we give a criterion to check whether a finite digraph is a Cayley graph of a finite Brandt semigroup. Also KelarevExpand
The commuting graph of the symmetric inverse semigroup
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.Expand
Minimal paths in the commuting graphs of semigroups
It is proved that for every positive integer n, there exists a semigroup S such that the diameter of G(S) is n, and it is shown that the shortest left path in S is the semigroup whose shortest right path has length n. Expand
On the Cayley Graphs of Brandt Semigroups
In this article, the Cayley graphs of Brandt semigroups are investigated. The basic structures and properties of this kind of Cayley graphs are given, and a necessary and sufficient condition isExpand