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math-ph2011★ 18 cited
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…
math-ph2011
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…