We investigate the laplacian spectrum of a quantum star graph with Robin condition applied to the interior vertices, and Dirichlet condition on the pendant vertices. Comparing with our previous results on laplacian spectrum for similar quantum graph with the Neumann-Kirchoff condition on interior vertices, we prove interlacing inequalities between the two spectra, that is the spectra from both the laplacian appear alternatingly.
REFERENCES
1.
G.
Berkolaiko
and P.
Kuchment
, Introduction to quantum graphs
, 186
(American Mathematical Soc.
, 2013
).2.
P.
Kuchment
, “Quantum graphs: I. some basic structures
,” Waves in Random media
14
, S107
(2003
).3.
M. J. I.
Burhan
, Y.
Soeharyadi
, and W. S.
Budhi
, “On eigenvalues of the laplacian with the dirichlet condition at end-vertices on simple quantum trees
,” in CONFERENCE PROCEEDINGS OF SCIENCE AND TECHNOLOGY
, Vol. 4
(2021
) pp. 284
–293
.4.
M. J. I.
Burhan
, Y.
Soeharyadi
, and W. S.
Budhi
, “Edge-based linear wave equations on quantum trees with dirichlet boundary conditions and its simulation
,” submitted (2022
).5.
M. A.
Klawonn
, “Spectral comparison of the standard laplacian on equilateral finite metric graphs subjected to kirchhoff and anti-kirchhoff vertex conditions
,” Hagen
: FernUniversität Hagen
(2019
).6.
G.
Berkolaiko
, “An elementary introduction to quantum graphs
,” Geometric and computational spectral theory
700
, 41
–72
(2017
).7.
F.
Aziz
, R. C.
Wilson
, and E. R.
Hancock
, “Graph characterization using gaussian wave packet signature,” in International Workshop on Similarity-Based Pattern Recognition
(Springer
, 2013
) pp. 176
–189
.8.
F.
Aziz
, R. C.
Wilson
, and E. R.
Hancock
, “A wave packet signature for complex networks
,” Journal of Complex Networks
7
, 346
–374
(2019
).9.
Ł. G.
Gajewski
, J.
Sienkiewicz
, and J. A.
Hołyst
, “Discovering hidden layers in quantum graphs
,” Physical Review E
104
, 034311
(2021
).10.
J.
Friedman
and J.-P.
Tillich
, “Wave equations for graphs and the edge-based laplacian
,” Pacific Journal of Mathematics
216
, 229
–266
(2004
).11.
R. C.
Wilson
, F.
Aziz
, and E. R.
Hancock
, “Eigenfunctions of the edge-based laplacian on a graph
,” Linear Algebra and its Applications
438
, 4183
–4189
(2013
).12.
F.
Zhang
, Matrix theory: basic results and techniques
(Springer
, 2011
).
This content is only available via PDF.
© 2024 AIP Publishing LLC.
2024
AIP Publishing LLC
You do not currently have access to this content.
