Strongly Regular Graphs with Maximal Energy

Research output: Working paperDiscussion paperOther research output

Abstract

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.
Original language English Tilburg Operations research 7 2007-37 Published - 2007

Publication series

Name CentER Discussion Paper 2007-37

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Strongly Regular Graph
Graph in graph theory
Energy
Absolute value
Equality
If and only if
Eigenvalue

Keywords

• Graph energy
• Strongly regular graph

Cite this

Haemers, W. H. (2007). Strongly Regular Graphs with Maximal Energy. (CentER Discussion Paper; Vol. 2007-37). Tilburg: Operations research.
Haemers, W.H. / Strongly Regular Graphs with Maximal Energy. Tilburg : Operations research, 2007. (CentER Discussion Paper).
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abstract = "The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.",
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author = "W.H. Haemers",
note = "Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 7",
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language = "English",
volume = "2007-37",
series = "CentER Discussion Paper",
publisher = "Operations research",
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Haemers, WH 2007 'Strongly Regular Graphs with Maximal Energy' CentER Discussion Paper, vol. 2007-37, Operations research, Tilburg.
Tilburg : Operations research, 2007. (CentER Discussion Paper; Vol. 2007-37).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Strongly Regular Graphs with Maximal Energy

AU - Haemers, W.H.

N1 - Subsequently published in Linear Algebra and its Applications, 2008 Pagination: 7

PY - 2007

Y1 - 2007

N2 - The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

AB - The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

KW - Graph energy

KW - Strongly regular graph

KW - Hadamard matrix.

M3 - Discussion paper

VL - 2007-37

T3 - CentER Discussion Paper

BT - Strongly Regular Graphs with Maximal Energy

PB - Operations research

CY - Tilburg

ER -

Haemers WH. Strongly Regular Graphs with Maximal Energy. Tilburg: Operations research. 2007. (CentER Discussion Paper).