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The generalized total graph of a commutative semiring

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Abstract

Let R be a commutative semiring with nonzero identity and H be a multiplicative-prime subset of R. The generalized total graph of a commutative semiring R is the (undirected) graph \(GT_{H}(R)\) whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if \(x+y\in H\). In this paper, we investigate the structure of \(GT_{H}(R)\) and we also study the two (induced) subgraphs \(GT_{H}(H)\) and \(GT_{H}(R{\setminus } H)\) with vertex-sets H and \(R{\setminus } H\).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Yahya Talebi & Atefeh Darzi

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  1. Yahya Talebi
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  2. Atefeh Darzi
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Correspondence to Yahya Talebi.

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Talebi, Y., Darzi, A. The generalized total graph of a commutative semiring. Ricerche mat 66, 579–589 (2017). https://doi.org/10.1007/s11587-017-0321-4

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  • DOI: https://doi.org/10.1007/s11587-017-0321-4

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