The cyclic graph of a semigroup
Sandeep Dalal, Jitender Kumar, Siddharth Singh

TL;DR
This paper studies the cyclic graph of a semigroup, classifies semigroups based on graph properties, and determines key graph invariants like clique and independence numbers.
Contribution
It provides classifications of semigroups with specific cyclic graph structures and calculates important graph parameters for various classes of semigroups.
Findings
Classified semigroups with complete, bipartite, tree, regular, null cyclic graphs.
Determined the clique number for any semigroup's cyclic graph.
Established bounds and characterized semigroups for the independence number in finite monogenic cases.
Abstract
The cyclic graph of a semigroup is the simple graph whose vertex set is and two vertices are adjacent if the subsemigroup generated by and is monogenic. In this paper, we classify the semigroup such that whose cyclic graph is complete, bipartite, tree, regular and a null graph, respectively. Further, we determine the clique number of for an arbitrary semigroup . We obtain the independence number of if is a finite monogenic semigroup. At the final part of this paper, we give bounds for independence number of if is a semigroup of bounded exponent and we also characterize the semigroups attaining the bounds.
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Taxonomy
Topicssemigroups and automata theory · Fuzzy and Soft Set Theory · Advanced Graph Theory Research
