@article {
author = {Ebrahimi Sarvandi, Z. and Ebrahimi Atani, S.},
title = {The total graph of a commutative semiring with respect to proper ideals},
journal = {Journal of Algebra and Related Topics},
volume = {3},
number = {2},
pages = {27-41},
year = {2015},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {},
abstract = {Let $I$ be a proper ideal of a commutative semiring $R$ and let $P(I)$ be the set of all elements of $R$ that are not prime to $I$. In this paper, we investigate the total graph of $R$ with respect to $I$, denoted by $T(\Gamma_{I} (R))$. It is the (undirected) graph with elements of $R$ as vertices, and for distinct $x, y \in R$, the vertices $x$ and $y$ are adjacent if and only if $x + y \in P(I)$. The properties and possible structures of the two (induced) subgraphs $P(\Gamma_{I} (R))$ and $\bar {P}(\Gamma_{I} (R))$ of $T(\Gamma_{I} (R))$, with vertices $P(I)$ and $R - P(I)$, respectively are studied.},
keywords = {Commutative semirings,Zero-divisor,Total graph},
url = {https://jart.guilan.ac.ir/article_1539.html},
eprint = {https://jart.guilan.ac.ir/article_1539_c4cf79602c757856bbf5ef810db8ebf5.pdf}
}