Clustering of spectra and fractals of regular graphs
| dc.creator | Ejov, V. | |
| dc.creator | Filar, J. A. | |
| dc.creator | Lucas, S. K. | |
| dc.creator | Zograf, P. | |
| dc.date | 2006-10-25 | |
| dc.date | 2007-08-30 | |
| dc.date.accessioned | 2026-07-07T08:26:33Z | |
| dc.date.available | 2026-07-07T08:26:33Z | |
| dc.description | We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labelled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind. | |
| dc.description | 10 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0610742 | |
| dc.identifier | http://arxiv.org/abs/math/0610742 | |
| dc.identifier | J. Math. Anal. Appl. 333 (2007) 236-246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136977 | |
| dc.subject | Combinatorics | |
| dc.subject | Statistics Theory | |
| dc.subject | 05C50; 62P99 | |
| dc.title | Clustering of spectra and fractals of regular graphs | |
| dc.type | text |