Complement of the generalized total graph of fields. Issue 3 (1st September 2020)

• Record Type: Journal Article
• Authors: Tamizh Chelvam, T.; Balamurugan, M.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 17:Issue 3(2020)
• Page Start: 730
• Page End: 733
• Publication Date: 2020-09-01
• Subjects: Generalized total graph -- field -- split -- chordal -- pancyclic -- perfect; Primary: 05C75 -- 05C25 -- Secondary:13A15 -- 13M05
• DOI: 10.1016/j.akcej.2019.12.005
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: Let R be a commutative ring and H be a multiplicative prime subset of R . The generalized total graph G T H ( R ) is the undirected simple graph with vertex set R and two distinct vertices x and y are adjacent if x + y ∈ H . For a field F, H = { 0 } is the only multiplicative prime subset of F and the corresponding generalized total graph is denoted by G T ( F ) . In this paper, we investigate several graph theoretical properties of G T ( F ) ¯, where G T ( F ) ¯ is the complement of the generalized total graph of F . In particular, we characterize all the fields for which G T ( F ) ¯ is unicyclic, split, chordal, claw-free, perfect and pancyclic.