On the clique number and independence number of the cyclic graph of a semigroup

被引：0

作者：

Dalal, Sandeep ^{[1
]}

Kumar, Jitender ^{[1
]}

Singh, Siddharth ^{[1
]}

机构：

[1] Birla Inst Technol & Sci Pilani, Dept Math, Pilani, India

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 05期

关键词：

Monogenic semigroup; completely 0-simple semigroup; cyclic graph; clique number; independence number; COMMUTING GRAPH; CAYLEY-GRAPHS; POWER GRAPHS;

D O I：

10.1142/S0219498824501019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The cyclic graph gamma(S) of a semigroup S is the simple undirected 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 determine the clique number of gamma(S) for an arbitrary semigroup S. Further, we obtain the independence number of gamma(S) if S is a finite monogenic semigroup. At the final part of this paper, we give bounds for independence number of gamma(S) if S is a semigroup of bounded exponent and we also characterize the semigroups attaining the bounds.

引用

页数：16