Show simple item record

dc.contributor.authorBiswas, Arindam
dc.date.accessioned2019-07-22T13:30:15Z
dc.date.available2019-07-22T13:30:15Z
dc.date.issued2019-07-22
dc.identifier.urihttp://publications.mfo.de/handle/mfo/2511
dc.description.abstractLet $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from $-1$. In this article we are interested in explicit bounds for the spectrum of these graphs. Specifically, we show that the non-trivial spectrum of the adjacency operator lies in the interval $\left[-1+\frac{h(\mathbb{G})^{4}}{\gamma}, 1-\frac{h(\mathbb{G})^{2}}{2d^{2}}\right]$, where $h(\mathbb{G})$ denotes the (vertex) Cheeger constant of the $d$ regular graph $C(G,S)$ with respect to a symmetric set $S$ of generators and $\gamma = 2^{9}d^{6}(d+1)^{2}$.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relationAlso published in: European Journal of Combinatorics 81(2019), pp. 298-308. doi:10.1016/j.ejc.2019.06.009. https://doi.org/10.1016/j.ejc.2019.06.009
dc.relation.ispartofseriesOberwolfach Preprints;2019,20
dc.subjectCheeger inequalityen_US
dc.subjectExpander graphsen_US
dc.subjectFinite Cayley graphsen_US
dc.titleOn a Cheeger Type Inequality in Cayley Graphs of Finite Groupsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2019-20
local.scientificprogramOWLF 2017en_US
local.series.idOWP-2019-20en_US
dc.identifier.urnurn:nbn:de:101:1-2019082214563824513644
local.date-range7 July - 7 October 2017en_US
dc.identifier.ppn167210954X


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record