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

  • Badawi A
Springer New York, (2014), 39-54
DOI: 10.1007/978-1-4939-0925-4_3
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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 .. .R// with vertices all elements of R, and two distinct vertices x and y are adjacent if and only if x C y 2 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.

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Badawi, A. (2014). On the Total Graph of a Ring and Its Related Graphs: A Survey. In Commutative Algebra (pp. 39–54). Springer New York. https://doi.org/10.1007/978-1-4939-0925-4_3

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