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

The vertex-isoperimetric number of the incidence and non-incidence graphs of unitals Des. Codes Cryptogr. https://doi.org/10.1007/s10623-018-0498-x The vertex-isoperimetric number of the incidence and non-incidence graphs of unitals 1 2 Alice M. W. Hui · Muhammad Adib Surani · Sanming Zhou Received: 1 December 2017 / Revised: 13 May 2018 / Accepted: 23 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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. Keywords Vertex-isoperimetric number · Unital · Incidence graph Mathematics Subject Classification 05C40 · 05B25 1 Introduction A unital is a 2-(n + 1, n + 1, 1) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Designs, Codes and Cryptography Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Combinatorics; Coding and Information Theory; Data Structures, Cryptology and Information Theory; Data Encryption; Discrete Mathematics in Computer Science; Information and Communication, Circuits
ISSN
0925-1022
eISSN
1573-7586
D.O.I.
10.1007/s10623-018-0498-x
Publisher site
See Article on Publisher Site

Abstract

Des. Codes Cryptogr. https://doi.org/10.1007/s10623-018-0498-x The vertex-isoperimetric number of the incidence and non-incidence graphs of unitals 1 2 Alice M. W. Hui · Muhammad Adib Surani · Sanming Zhou Received: 1 December 2017 / Revised: 13 May 2018 / Accepted: 23 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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. Keywords Vertex-isoperimetric number · Unital · Incidence graph Mathematics Subject Classification 05C40 · 05B25 1 Introduction A unital is a 2-(n + 1, n + 1, 1)

Journal

Designs, Codes and CryptographySpringer Journals

Published: May 31, 2018

References

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