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The Total Graphs of Finite Commutative Semirings

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Abstract

Anderson and Badawi (J Algebra 320(7):2706–2719, 2008) characterized all commutative rings having total graphs without any 3-cycles. In this paper we expand those results to the semiring setting and obtain the characterization of finite commutative semirings having total graphs without any 3-cycles.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000, Ljubljana, Slovenia

    David Dolžan

  2. Faculty of Computer and Information Science, University of Ljubljana, Večna pot 113, 1000, Ljubljana, Slovenia

    Polona Oblak

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  1. David Dolžan
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  2. Polona Oblak
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Correspondence to Polona Oblak.

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Dolžan, D., Oblak, P. The Total Graphs of Finite Commutative Semirings. Results Math 72, 193–204 (2017). https://doi.org/10.1007/s00025-016-0595-y

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  • DOI: https://doi.org/10.1007/s00025-016-0595-y

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