Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On the intersection ideal graph of semigroups
Authors: B. Baloda and J. Kumar
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Abstract
The intersection ideal graph Γ(S) of a semigroup S is a simple undirected graph whose vertices are all nontrivial left ideals of S and two distinct left ideals I, J are adjacent if and only if their intersection is nontrivial. In this paper, we investigate the connectedness of Γ(S). We show that if Γ(S) is connected, then the diameter of Γ(S) is at most two. Further, we classify the semigroups S in terms of their ideals such that the diameter of Γ(S) is two. We obtain the domination number, independence number, girth and the strong metric dimension of Γ(S). We have also investigated the completeness, planarity and perfectness of Γ(S). We show that if S is a completely simple semigroup, then Γ(S) is weakly perfect. More over, in this article, we give an upper bound of the chromatic number of Γ(S). Finally, if S is the union of n minimal left ideals, then we obtain the metric dimension and the automorphism group of Γ(S).Department of Mathematics,
Birla Institute of Technology and Science Pilani,
Pilani, India
E-mail: ,
Birla Institute of Technology and Science Pilani,
Pilani, India
E-mail: ,
DOI
https://doi.org/10.56415/qrs.v31.01Fulltext
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Contents
- On the intersection ideal graph of semigroups
- On topological completely inverse AG**-groupoids
- A double construction of quadratic anticenter-symmetric Jacobi-Jordan algebras
- On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography
- Semigroups in which the radical of every interior ideal is a subsemigroup
- Branched covers induced by semisymmetric quasigroup homomorphisms
- General form of the automorphism group of bicyclic graphs
- Weakly quasi invo-clean rings
- On central digraphs constructed from left loops and loops
- Some types of interior filters in quasi-ordered semigroups
- Injective and projective poset acts
