Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On the local geometry of graphs in terms of their spectra
MIT, Dept Math, Cambridge, MA 02139 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). MIT, Dept Math, Cambridge, MA 02139 USA..ORCID iD: 0000-0003-3071-9393
2019 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 81, p. 378-393Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose G(1), G(2), G(3), ... is a sequence of finite and connected graphs that share a common universal cover T and such that the proportion of eigenvalues of G(n) that lie within the support of the spectrum of T tends to 1 in the large n limit. This is a weak notion of being Ramanujan. We prove such a sequence of graphs is asymptotically locally tree-like. This is deduced by way of an analogous theorem proved for certain infinite sofic graphs and unimodular networks, which extends results for regular graphs and certain infinite Cayley graphs.

Place, publisher, year, edition, pages
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD , 2019. Vol. 81, p. 378-393
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-259409DOI: 10.1016/j.ejc.2019.07.001ISI: 000482519400024Scopus ID: 2-s2.0-85068503220OAI: oai:DiVA.org:kth-259409DiVA, id: diva2:1354122
Note

QC 20190924

Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-09-24Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Rahman, Mustazee

Search in DiVA

By author/editor
Rahman, Mustazee
By organisation
Mathematics (Div.)
In the same journal
European journal of combinatorics (Print)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf