## Abstract

We introduce and investigate the total graph of a commutative semiring with non-zero identity. The main purpose of this paper is to extend the definition and some results given in [2] to a more general semiring case.

Show Summary Details# The Total Graph of a Commutative Semiring

#### Open Access

## Abstract

## About the article

More options …# Analele Universitatii "Ovidius" Constanta - Seria Matematica

### The Journal of "Ovidius" University of Constanta

More options …

Editor-in-Chief: Flaut, Cristina

1 Issue per year

IMPACT FACTOR 2016: 0.422

CiteScore 2016: 0.56

SCImago Journal Rank (SJR) 2016: 0.346

Source Normalized Impact per Paper (SNIP) 2016: 0.966

Mathematical Citation Quotient (MCQ) 2016: 0.10

We introduce and investigate the total graph of a commutative semiring with non-zero identity. The main purpose of this paper is to extend the definition and some results given in [2] to a more general semiring case.

Keywords: Semiring; total graph; k-ideal; Q-ideal

[1] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra, 159 (1993), 500-514.Google Scholar

[2] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320 (2008), 2706-2719.Web of ScienceGoogle Scholar

[3] D. F. Anderson and P. F. Livingston, The zero-divisor graph of a com- mutative ring, J. Algebra, 217 (1999), 437-447.Web of ScienceGoogle Scholar

[4] P. J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416.Google Scholar

[5] I. Beck, Coloring of a commutative ring, J. Algebra, 116 (1988), 208-226.Google Scholar

[6] S. Ebrahimi Atani, The ideal theory in quotients of commutative semir- ings, Glas. Math., 42 (2007), 301-308.Google Scholar

[7] S. Ebrahimi Atani, The zero-divisor graph with respect to ideals of a com- mutative semiring, Glas. Math., 43 (2008), 309-320.Google Scholar

[8] S. Ebrahimi Atani, An ideal-based zero-divisor graph of a commutative semiring, Glas. Math., 44 (1) (2009), 141-153.Google Scholar

[9] S. Ebrahimi Atani and R. Ebrahimi Atani, Some remarks on partitioning semirings, An. St. Univ. Ovidius Constanta, 18(1) (2010), 49-62.Google Scholar

[10] S. Ebrahimi Atani and S. Habibi, The total torsion element graph of a module over a commutative ring, An. St. Univ. Ovidius Constanta, 19(1) (2011), 23-34.Google Scholar

[11] J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer Science, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific and Technical, Harlow UK, (1992).Google Scholar

[12] J. S. Golan, Semirings and their Applications, Kluwer Academic Publish- ers, Dordrecht, (1999).Google Scholar

[13] S. B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra, 30(7) (2002), 3533-3558. Google Scholar

**Published Online**: 2013-09-19

**Published in Print**: 2013-06-01

**Citation Information: **Analele Universitatii "Ovidius" Constanta - Seria Matematica, Volume 21, Issue 2, Pages 21–33, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/auom-2013-0021.

This content is open access.

## Comments (0)