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On the Inclusion Ideal Graph of Semigroups.
- Source :
-
Algebra Colloquium . Sep2023, Vol. 30 Issue 3, p411-428. 18p. - Publication Year :
- 2023
-
Abstract
- The inclusion ideal graph I n (S) of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I , J are adjacent if and only if either I ⊂ J or J ⊂ I. The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of I n (S). We investigate the connectedness of I n (S) and show that the diameter of I n (S) is at most 3 if it is connected. We also obtain a necessary and sufficient condition of S such that the clique number of I n (S) is the number of minimal left ideals of S. Further, various graph invariants of I n (S) , viz. perfectness, planarity, girth, etc., are discussed. For a completely simple semigroup S , we investigate properties of I n (S) including its independence number and matching number. Finally, we obtain the automorphism group of I n (S). [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTOMORPHISM groups
*UNDIRECTED graphs
*CAYLEY graphs
*PLANAR graphs
Subjects
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 30
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 170750490
- Full Text :
- https://doi.org/10.1142/S1005386723000342