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Spectral Threshold for Extremal Cyclic Edge-Connectivity.
- Source :
-
Graphs & Combinatorics . Nov2021, Vol. 37 Issue 6, p2079-2093. 15p. - Publication Year :
- 2021
-
Abstract
- The universal cyclic edge-connectivity of a graph G is the least k such that there exists a set of k edges whose removal disconnects G into components where every component contains a cycle. We show that for graphs of minimum degree at least 3 and girth g at least 4, the universal cyclic edge-connectivity is bounded above by (Δ - 2) g where Δ is the maximum degree. We then prove that if the second eigenvalue of the adjacency matrix of a d-regular graph of girth g ≥ 4 is sufficiently small, then the universal cyclic edge-connectivity is (d - 2) g , providing a spectral condition for when this upper bound on universal cyclic edge-connectivity is tight. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 37
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 153556106
- Full Text :
- https://doi.org/10.1007/s00373-021-02333-6