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Complement of the Generalized Total Graph of Commutative Rings – A Survey

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Algebra and Related Topics with Applications (ICARTA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 392))

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Abstract

There are so many graph constructions from algebraic structures. In particular, graphs from commutative rings are extensively studied. Zero-divisor graphs from commutative rings are the first graph construction in this regard. In the zero divisor graph of a commutative ring, edges are constructed through multiplication of the underlying ring. In variation to this, several graphs are constructed using addition of a commutative ring. The first graph construction using addition is the total graph and later generalized total graphs from commutative rings are introduced and studied. In this paper, we make a survey of results obtained on the complement of the generalized total graph of commutative rings as well as fields.

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Acknowledgements

This research work is supported by CSIR Emeritus Scientist Scheme (No. 21 (1123)/20/EMR-II) of Council of Scientific and Industrial Research, Government of India.

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Authors and Affiliations

  1. Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, 627012, Tamil Nadu, India

    T. Tamizh Chelvam

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  1. T. Tamizh Chelvam
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Correspondence to T. Tamizh Chelvam .

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  1. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Mohammad Ashraf

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Asma Ali

  3. Department of Engineering, University of Messina, Messina, Italy

    Vincenzo De Filippis

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Tamizh Chelvam, T. (2022). Complement of the Generalized Total Graph of Commutative Rings – A Survey. In: Ashraf, M., Ali, A., De Filippis, V. (eds) Algebra and Related Topics with Applications. ICARTA 2019. Springer Proceedings in Mathematics & Statistics, vol 392. Springer, Singapore. https://doi.org/10.1007/978-981-19-3898-6_36

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