Graphs and Combinatorics

, Volume 34, Issue 2, pp 339–347 | Cite as

Total Colorings of Product Graphs

  • J. Geetha
  • K. Somasundaram
Original Paper


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.


Product graphs Direct product Strong product Lexicographic product Total coloring 



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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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsAmrita School of Engineering-CoimbatoreCoimbatoreIndia

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