Isospectral graphs with identical nodal counts

Idan Oren; Ram Band

doi:10.1088/1751-8113/45/13/135203

Isospectral graphs with identical nodal counts

Idan Oren, Ram Band

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 892133). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs.

Original language	English
Article number	135203
Journal	JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume	45
Issue number	13
DOIs	https://doi.org/10.1088/1751-8113/45/13/135203
State	Published - 6 Apr 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/45/13/135203

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abstract = "According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 892133). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs.",

author = "Idan Oren and Ram Band",

note = "ISF [169/09]; EPSRC [EP/H028803/1]We warmly thank Uzy Smilansky for his continuous support, significant encouragement and for many invaluable discussions. We acknowledge Amit Godel for helping us revive the proof for equation (8). The work was supported by ISF grant 169/09. RB is supported by EPSRC, grant number EP/H028803/1.",

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AB - According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 892133). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs.

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M3 - مقالة

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ER -

Isospectral graphs with identical nodal counts

Abstract

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