# Total graph of a commutative semiring with respect to singular ideal

## DOI:

https://doi.org/10.22199/issn.0717-6279-2020-03-0032## Keywords:

Semiring, Total graph, Singular ideal, Induced subgraph## Abstract

Let S be a commutative semiring with unity. The singular ideal Z(S) of S is defined as Z(S) = {s ? S | sK = 0 for some essential ideal K of S}. In this paper, we introduce the notion of total graph of a commutative semiring with respect to the singular ideal. We define this graph as the undirected graph T(?(S)) with all elements of S as vertices and any two distinct vertices x and y are adjacent if and only if x + y ? Z(S). We discuss various characteristics of this total graph and also characterize some important properties of certain induced subgraphs of this total graph.## References

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*Proyecciones (Antofagasta, On line)*, vol. 39, no. 3, pp. 517-527, Jun. 2020.

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Copyright (c) 2020 Nabanita Goswami, Helen K. Saikia

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