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Graphs and Combinatorics

, Volume 35, Issue 3, pp 779–785 | Cite as

The Cyclic Edge-Connectivity of Strongly Regular Graphs

  • Wenqian ZhangEmail author
Original Paper
  • 87 Downloads

Abstract

Let G be a connected graph. An edge cut set M of G is a cyclic edge cut set if there are at least two components of \(G-M\) which contain a cycle. The cyclic edge-connectivity of G is the minimum cardinality of a cyclic edge cut set (if exists) of G. In this paper, we show that the cyclic edge-connectivity of a connected strongly regular graph G (not \(K_{3,3}\)) of degree \(k\ge 3\) with girth c is equal to \((k-2)c\), where \(c=3, 4\) or 5. Moreover, if G is not the triangular graph srg-(10, 6, 3, 4), the complete multi-partite graph \(K_{2,2,2,2}\) or the lattice graph srg-(16, 6, 2, 2), then each cyclic edge cut set of size \((k-2)c\) is precisely the set of edges incident with a cycle of length c in G.

Keywords

Strongly regular graph Eigenvalue Edge cut set Cyclic edge-connectivity 

Mathematics Subject Classification

05C40 05C50 05C75 

Notes

Acknowledgements

The author would like to thank the editors and the anonymous referees for their helpful comments on improving the representation of the paper.

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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