Computing the size of zero divisor graphs. Issue 4 (18th May 2020)

• Record Type: Journal Article
• Authors: Mukhtar, Aamir; Murtaza, Rashid; Rehman, Shafiq U.; Usman, Saima; Baig, Abdul Qudair
• Is Part Of: Journal of information & optimization sciences. Volume 41:Issue 4(2020)
• Page Start: 855
• Page End: 864
• Publication Date: 2020-05-18
• Subjects: Primary 05C25; Finite rings -- Zero divisor graph -- GCD-Sum function; Electronic data processing -- Periodicals; Information science -- Periodicals; Mathematical optimization -- Periodicals; 519.6
• DOI: 10.1080/02522667.2020.1745378
• Languages: English
• ISSNs: 0252-2667

Abstract

Abstract: A recent subject of study linking commutative ring theory with graph theory has been the concept of the zero divisor graph of a commutative ring. The zero divisor graph of a commutative ring exhibits a remarkable amount of graphical structure. Let G ( R ) be the zero divisor graph introduced by Beck [9], whose vertices are the elements of a ring R such that two distinct vertices x, y are adjacent provided that xy = 0 . Let Г( R ) be the zero divisor graph introduced by Anderson, Livingston [5] whose vertices are the non-zero zero divisors of the ring R such that two distinct vertices x, y are adjacent provided that xy = 0 . Here, the authors investigate the size of the graphs G(ℤ n ), Г(ℤ n ).