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Total Colorings of Product Graphs

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Abstract

A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove Behzad–Vizing conjecture for product graphs. In particular, we obtain the tight bound for certain classes of graphs.

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Acknowledgements

We are grateful to the reviewers for their valuable and helpful comments which lead to the improvement of this paper. This work was supported by SERB (No. SB/S4/MS:867/14).

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering-Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India

    J. Geetha & K. Somasundaram

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  1. J. Geetha
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  2. K. Somasundaram
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Correspondence to J. Geetha.

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Geetha, J., Somasundaram, K. Total Colorings of Product Graphs. Graphs and Combinatorics 34, 339–347 (2018). https://doi.org/10.1007/s00373-018-1876-x

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