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Graphs and Combinatorics

, Volume 35, Issue 6, pp 1273–1291 | Cite as

On the Integrability of Strongly Regular Graphs

  • Jack H. Koolen
  • Masood Ur Rehman
  • Qianqian YangEmail author
Original Paper
  • 121 Downloads

Abstract

Koolen et al. showed that if a connected graph with smallest eigenvalue at least \(-3\) has large minimal valency, then it is 2-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.

Keywords

Strongly regular graph Lattice s-Integrability 

Mathematics Subject Classification

05C50 05E30 11H99 

Notes

Acknowledgements

The first author J.H. Koolen is partially supported by the National Natural Science Foundation of China (Grant No. 11471009 and Grant No. 11671376) and Anhui Initiative in Quantum Information Technologies (No. AHY150000). The second author M.U. Rehman is supported by the Chinese Scholarship Council at USTC, China. The corresponding author Q. Yang is partially supported by the Chinese Scholarship Council (No. 201806340049). We also would like to thank Akihiro Munemasa for pointing out that one can extend the complement of the McLaughlin graph to obtain a slightly better lower bound.

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Wen-Tsun Wu Key Laboratory of CAS, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

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