Complement of the generalized total graph of fields. Issue 3 (1st September 2020) - Tamizh Chelvam, T.; Balamurugan, M.
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.