31 citations · 62 across the 5 of their papers we have counts for
5 papers
Isospectral graphs with identical nodal counts
Idan Oren, Ram Band
According to a recent conjecture, isospectral objects have different nodal count sequences. We study generalized Laplacians on discrete graphs, and use them to construct the first…
Periodic Walks on Large Regular Graphs and Random Matrix Theory
Idan Oren, Uzy Smilansky
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of -p…
Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II)
Idan Oren, Uzy Smilansky
Following the derivation of the trace formulae in the first paper in this series, we establish here a connection between the spectral statistics of random regular graphs and the pr…
Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (I)
Idan Oren, Amit Godel, Uzy Smilansky
Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend…
Nodal domains on graphs - How to count them and why?
Ram Band, Idan Oren, Uzy Smilansky
The purpose of the present manuscript is to collect known results and present some new ones relating to nodal domains on graphs, with special emphasize on nodal counts. Several met…