Developments on Spectral Characterizations of Graphs

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Abstract

In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages17
Volume2007-33
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-33

Fingerprint

Graph in graph theory
Laplacian Matrix
Adjacency Matrix
Linear algebra

Keywords

  • Spectra of graphs
  • Cospectral graphs
  • Generalized adjacency matrices
  • Distance-regular graphs

Cite this

van Dam, E. R., & Haemers, W. H. (2007). Developments on Spectral Characterizations of Graphs. (CentER Discussion Paper; Vol. 2007-33). Tilburg: Operations research.
van Dam, E.R. ; Haemers, W.H. / Developments on Spectral Characterizations of Graphs. Tilburg : Operations research, 2007. (CentER Discussion Paper).
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abstract = "In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50",
keywords = "Spectra of graphs, Cospectral graphs, Generalized adjacency matrices, Distance-regular graphs",
author = "{van Dam}, E.R. and W.H. Haemers",
note = "Subsequently published in Discrete Mathematics, 2009 Pagination: 17",
year = "2007",
language = "English",
volume = "2007-33",
series = "CentER Discussion Paper",
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van Dam, ER & Haemers, WH 2007 'Developments on Spectral Characterizations of Graphs' CentER Discussion Paper, vol. 2007-33, Operations research, Tilburg.

Developments on Spectral Characterizations of Graphs. / van Dam, E.R.; Haemers, W.H.

Tilburg : Operations research, 2007. (CentER Discussion Paper; Vol. 2007-33).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Developments on Spectral Characterizations of Graphs

AU - van Dam, E.R.

AU - Haemers, W.H.

N1 - Subsequently published in Discrete Mathematics, 2009 Pagination: 17

PY - 2007

Y1 - 2007

N2 - In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50

AB - In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50

KW - Spectra of graphs

KW - Cospectral graphs

KW - Generalized adjacency matrices

KW - Distance-regular graphs

M3 - Discussion paper

VL - 2007-33

T3 - CentER Discussion Paper

BT - Developments on Spectral Characterizations of Graphs

PB - Operations research

CY - Tilburg

ER -

van Dam ER, Haemers WH. Developments on Spectral Characterizations of Graphs. Tilburg: Operations research. 2007. (CentER Discussion Paper).