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
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
收藏
页数:16
相关论文
共 21 条
[1]  
Aalipour G, 2017, ELECTRON J COMB, V24
[2]   Noncyclic graph of a group [J].
Abdollahi, A. ;
Hassanabadi, A. Mohammadi .
COMMUNICATIONS IN ALGEBRA, 2007, 35 (07) :2057-2081
[3]   On cyclic graphs of finite semigroups [J].
Afkhami, M. ;
Jafarzadeh, A. ;
Khashyarmanesh, K. .
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (07)
[4]   The commuting graph of the symmetric inverse semigroup [J].
Araujo, Joao ;
Bentz, Wolfram ;
Konieczny, Janusz .
ISRAEL JOURNAL OF MATHEMATICS, 2015, 207 (01) :103-149
[5]   Minimal paths in the commuting graphs of semigroups [J].
Araujo, Joao ;
Kinyon, Michael ;
Konieczny, Janusz .
EUROPEAN JOURNAL OF COMBINATORICS, 2011, 32 (02) :178-197
[6]  
Bosak J., 1964, GRAPHS SEMIGROUPS
[7]   Undirected power graphs of semigroups [J].
Chakrabarty, Ivy ;
Ghosh, Shamik ;
Sen, M. K. .
SEMIGROUP FORUM, 2009, 78 (03) :410-426
[8]  
Dalal S., 2022, ALGEBRA C
[9]   Chromatic Number of the Cyclic Graph of Infinite Semigroup [J].
Dalal, Sandeep ;
Kumar, Jitender .
GRAPHS AND COMBINATORICS, 2020, 36 (01) :109-113
[10]   ON THE CAYLEY GRAPHS OF BRANDT SEMIGROUPS [J].
Hao, Yifei ;
Gao, Xing ;
Luo, Yanfeng .
COMMUNICATIONS IN ALGEBRA, 2011, 39 (08) :2874-2883