On the Total Graph of a Ring and Its Related Graphs: A Survey

Ayman Badawi ()
Additional contact information
Ayman Badawi: American University of Sharjah, Department of Mathematics and Statistics

A chapter in Commutative Algebra, 2014, pp 39-54 from Springer

Abstract: Abstract Let R be a (commutative) ring with nonzero identity and Z(R) be the set of all zero divisors of R. The total graph of R is the simple undirected graph T(Γ(R)) with vertices all elements of R, and two distinct vertices x and y are adjacent if and only if x + y ∈ Z(R). This type of graphs has been studied by many authors. In this paper, we state many of the main results on the total graph of a ring and its related graphs.

Keywords: Total graph; Zero divisors; Diameter; Girth; Connected graph Genus; Generalized total graph; Dominating set; Clique; Chromatic number; 13A15; 13B99; 05C99 (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:sprchp:978-1-4939-0925-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9781493909254

DOI: 10.1007/978-1-4939-0925-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().