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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2014; 51(3): 593-607

Printed May 1, 2014

https://doi.org/10.4134/JKMS.2014.51.3.593

Copyright © The Korean Mathematical Society.

Total graph of a Commutative semiring with respect to identity-summand elements

Shahabaddin Ebrahimi Atani, Saboura Dolati Pish Hesari, and Mehdi Khoramdel

University of Guilan, University of Guilan, University of Guilan

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Let $R$ be an $I$-semiring and $S(R)$ be the set of all identity-summand elements of $R$. In this paper we introduce the total graph of $R$ with respect to identity-summand elements, denoted by $T(\Gamma(R))$, and investigate basic properties of $S(R)$ which help us to gain interesting results about $T(\Gamma(R))$ and its subgraphs.

Keywords: I-semiring, minimal prime co-ideal, identity-summand graph, total identity-summand graph

MSC numbers: 16Y60, 05C62

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