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On Vertex Types of Graphs

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Abstract

The vertices of a graph are classified into seven types by J.T. Hedetniemi, S.M. Hedetniemi, S.T. Hedetniemi and T.M. Lewis and they ask the following questions: (1) What is the smallest order n of a graph having \(n-2\) very typical vertices or \(n-2\) typical vertices? (2) What is the smallest order of a pantypical graph? We answer these two questions and determine all the possible orders of the graphs in these three classes in this paper.

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References

  1. Hedetniemi, J.T., Hedetniemi, S.M., Hedetniemi, S.T., Lewis, T.M.: Analyzing graphs by degrees. AKCE Int. J. Graphs Comb. 10(4), 359–375 (2013)

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  2. Kamath, S.S., Bhat, R.S.: On strong (weak) independent sets and vertex coverings of a graph. Discrete Math. 307(9–10), 1136–1145 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Sampathkumar, E., Latha, L.P.: Strong weak domination and domination balance in a graph. Discrete Math. 161(1–3), 235–242 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Professor Wendy Myrvold wrote a computer program, which found all smallest pantypical graphs.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Pu Qiao & Xingzhi Zhan

Authors
  1. Pu Qiao
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  2. Xingzhi Zhan
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Corresponding author

Correspondence to Pu Qiao.

Additional information

This research was supported by the Shanghai SF grant 15ZR1411500, Science and Technology Commission of Shanghai Municipality (STCSM) Grant 13dz2260400 and the NSFC Grant 11671148.

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Qiao, P., Zhan, X. On Vertex Types of Graphs. Graphs and Combinatorics 34, 889–900 (2018). https://doi.org/10.1007/s00373-018-1919-3

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  • DOI: https://doi.org/10.1007/s00373-018-1919-3

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