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Zero-divisor graphs and total coloring conjecture

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Abstract

In this paper, we prove that the zero-divisor graphs of a special class of pseudocomplemented posets satisfy the total coloring conjecture. Also, we determine the edge chromatic number of the zero-divisor graphs of this special class of pseudocomplemented posets. These results are applied to zero-divisor graphs of finite reduced commutative rings.

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Acknowledgements

The authors gratefully acknowledge the financially support by Department of Science and Technology via DST-SERB Project EMR/2016/005162. Also, the authors would like to thank the referee for his/her valuable suggestions which improved the presentation of the paper. The first author would like to dedicate this research work to Late Somnath Narale for his constant support and encouragement.

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Authors and Affiliations

  1. Department of Mathematics, Savitribai Phule Pune University, Pune, 411007, Maharashtra, India

    Nilesh Khandekar & Vinayak Joshi

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  1. Nilesh Khandekar
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  2. Vinayak Joshi
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Correspondence to Vinayak Joshi.

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Communicated by A. Di Nola.

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Khandekar, N., Joshi, V. Zero-divisor graphs and total coloring conjecture. Soft Comput 24, 18273–18285 (2020). https://doi.org/10.1007/s00500-020-05344-2

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