TY - JOUR
T1 - GAP SETS FOR THE SPECTRA OF CUBIC GRAPHS
AU - Kollár, Alicia J.
AU - Sarnak, Peter
N1 - Publisher Copyright:
© 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0).
PY - 2021
Y1 - 2021
N2 - We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals (2√2, 3) and [−3, −2) achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [−3, 3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in [−3, 3) can be gapped by planar cubic graphs. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.
AB - We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals (2√2, 3) and [−3, −2) achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [−3, 3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in [−3, 3) can be gapped by planar cubic graphs. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.
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U2 - 10.1090/cams/3
DO - 10.1090/cams/3
M3 - Article
AN - SCOPUS:105003025118
SN - 2692-3688
VL - 1
SP - 1
EP - 38
JO - Communications of the American Mathematical Society
JF - Communications of the American Mathematical Society
ER -