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The vertex-isoperimetric number of the incidence and non-incidence graphs of unitals

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Abstract

We derive upper and lower bounds for the vertex-isoperimetric number of the incidence graphs of unitals and determine its order of magnitude. In the case when a unital contains sufficiently large arcs, these bounds agree and give rise to the precise value of this parameter. In particular, we obtain the exact value of the vertex-isoperimetric number of the incidence graphs of classical unitals and a certain subfamily of BM-unitals. In the case when the maximum size of arcs in the unital is relatively small, we obtain an upper bound for this parameter in terms of the vertex-isoperimetric number of the incidence graph. We also determine the exact value of the vertex-isoperimetric number of the non-incidence graph of any unital.

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Acknowledgements

A. Hui was supported by the Young Scientists Fund (Grant No. 11701035) of the National Natural Science Foundation of China. S. Zhou was supported by a Future Fellowship (FT110100629) of the Australian Research Council.

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Correspondence to Sanming Zhou.

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Communicated by D. Ghinelli.

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Hui, A.M.W., Surani, M.A. & Zhou, S. The vertex-isoperimetric number of the incidence and non-incidence graphs of unitals. Des. Codes Cryptogr. 87, 957–970 (2019). https://doi.org/10.1007/s10623-018-0498-x

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  • DOI: https://doi.org/10.1007/s10623-018-0498-x

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