Symmetric graph of a ring with involution

W. M. Fakeih () and T. Asir ()
Additional contact information
W. M. Fakeih: King Abdulaziz University
T. Asir: Madurai Kamaraj University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 288-296

Abstract: Abstract Let R be a ring with involution $$*$$ ∗ . The graph $$S\varGamma ^*(R)$$ S Γ ∗ ( R ) is obtained by letting all the elements of nonzero zero-divisors of R to be the vertices and defining distinct vertices x and y to be adjacent if $$xy=0$$ x y = 0 (or $$yx=0$$ y x = 0 ) and $$yx^*=0$$ y x ∗ = 0 . The graph $$S\varGamma ^*(R)$$ S Γ ∗ ( R ) is a generalization of the well known zero-divisor graph of R. In this paper, some graph theoretical properties of the $$*-$$ ∗ - symmetric graph are studied.

Keywords: Zero-divisors; Involution; $$*-$$ ∗ - ring; Zero-divisor graphs; Diameter of a graph; Primary: 13A15; 13M05; Secondary: 05C75; 05C25 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-022-00253-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:54:y:2023:i:1:d:10.1007_s13226-022-00253-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-022-00253-6

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().