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The graphs with all but two eigenvalues equal to - 2 or 0

Cioabă,Sebastian M.
; 
Haemers,Willem H.
; 
Vermette,Jason R.
Abstract
We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from $\pm 1$ and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen.
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Date
2017-07-01
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Tilburg University Research Output Collection
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Keywords
Adjacency matrix, Graph spectrum, Spectral characterizations
Citation
Cioabă, S M, Haemers, W H & Vermette, J R 2017, 'The graphs with all but two eigenvalues equal to - 2 or 0', Designs Codes and Cryptography, vol. 84, no. 1-2, pp. 153-163. https://doi.org/10.1007/s10623-016-0241-4
URI
https://hdl.handle.net/20.500.14602/69576
License
info:eu-repo/semantics/openAccess
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