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Adjacency Matrix
Degree Sequence
Eigenvectors
Graph Laplacian
Spectral Radius
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Semiregular trees with minimal Laplacian spectral radius
Semiregular trees with minimal Laplacian spectral radius,10.1016/j.laa.2009.06.014,Linear Algebra and Its Applications,Türker Bıyıkoğlu,Josef Leydold
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Semiregular trees with minimal Laplacian spectral radius
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Citations: 1
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Türker Bıyıkoğlu
,
Josef Leydold
A semiregular tree is a tree where all nonpendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency/Laplacian)
spectral radius
is a caterpillar. Counter examples show that the result cannot be generalized to the class of trees with a given (nonconstant) degree sequence.
Journal:
Linear Algebra and Its Applications  LINEAR ALGEBRA APPL
, vol. 432, no. 9, pp. 23352341, 2010
DOI:
10.1016/j.laa.2009.06.014
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References
(9)
Graphs with Given Degree Sequence and Maximal Spectral Radius
(
Citations: 7
)
Tuerker Biyikoglu
,
Josef Leydold
Published in 2006.
LARGEST EIGENVALUES OF THE DISCRETE PLAPLACIAN OF TREES WITH DEGREE SEQUENCES
(
Citations: 3
)
MARC HELLMUTH
,
JOSEF LEYDOLD
Published in 2009.
Matrix analysis
(
Citations: 1137
)
Roger A. Horn
,
Charles R. Johnson
Published in 1990.
The minimal Laplacian spectral radius of trees with a given diameter
(
Citations: 2
)
Ruifang Liu
,
Zhonghua Lu
,
Jinlong Shu
Journal:
Theoretical Computer Science  TCS
, vol. 410, no. 1, pp. 7883, 2009
On the index of caterpillars
(
Citations: 11
)
Slobodan K. Simic
,
Enzo Maria Li Marzi
,
Francesco Belardo
Journal:
Discrete Mathematics  DM
, vol. 308, no. 23, pp. 324330, 2008
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(1)
The acceleration of implant osseointegration by liposomal Wnt3a
(
Citations: 1
)
Antoine Popelut
,
Scott M. Rooker
,
Philipp Leucht
,
Marie Medio
,
John B. Brunski
,
Jill A. Helms
Journal:
Biomaterials
, vol. 31, no. 35, pp. 91739181, 2010