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Graphs of Order n with Determining Number \(n{-}3\)

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Abstract

A set S of vertices is a determining set of a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of G, denoted by \(\mathrm{Det}(G)\), is the smallest size of a determining set. In this paper, we give an explicit characterization for connected graphs of order n with determining number \(n-3\)

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Acknowledgements

We would like to give thanks to the referee for his careful reading and helpful comments, which makes our article more readable.

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China

    Dein Wong, Yuanshuai Zhang & Zhijun Wang

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  1. Dein Wong
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  2. Yuanshuai Zhang
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  3. Zhijun Wang
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Correspondence to Dein Wong.

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Supported by the National Natural Science Foundation of China (No.11971474).

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Wong, D., Zhang, Y. & Wang, Z. Graphs of Order n with Determining Number \(n{-}3\). Graphs and Combinatorics 37, 1179–1189 (2021). https://doi.org/10.1007/s00373-021-02300-1

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