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Gap sets for the spectra of cubic graphs
- Source :
- Communications of the American Mathematical Society. 1:1-38
- Publication Year :
- 2021
- Publisher :
- American Mathematical Society (AMS), 2021.
-
Abstract
- 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 ) (2 \sqrt {2},3) and [ − 3 , − 2 ) [-3,-2) achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [ − 3 , 3 ] [-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 ) [-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.
- Subjects :
- Mathematics - Number Theory
FOS: Physical sciences
Mathematical Physics (math-ph)
Spectral line
Ramanujan's sum
law.invention
Mathematics - Spectral Theory
Combinatorics
symbols.namesake
Planar
law
Line graph
FOS: Mathematics
symbols
Mathematics - Combinatorics
Cubic graph
Point (geometry)
Combinatorics (math.CO)
Number Theory (math.NT)
Adjacency matrix
Spectral Theory (math.SP)
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 26923688
- Volume :
- 1
- Database :
- OpenAIRE
- Journal :
- Communications of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....8df12ed25300c40cc2c8c37393f90647