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dc.contributor.authorBiswas, Arindam
dc.contributor.authorSaha, Jyoti Prakash
dc.date.accessioned2019-07-31T06:18:57Z
dc.date.available2019-07-31T06:18:57Z
dc.date.issued2019-07-31
dc.identifier.urihttp://publications.mfo.de/handle/mfo/2512
dc.description.abstractLet $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $|S| = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is non-bipartite, then the spectrum of its normalised adjacency operator is bounded away from $-1$. We also establish an explicit lower bound for the spectrum of these graphs, namely, the non-trivial eigenvalues of the normalised adjacency operator lies in the interval $\left(-1+\frac{h(G)^{4}}{\eta}, 1-\frac{h(G)^{2}}{2d^{2}}\right]$, where $h(G)$ denotes the (vertex) Cheeger constant of the $d$-regular graph $C_{\Sigma}(G,S)$ and $\eta = 2^{9}d^{8}$. Further, we improve upon a recently obtained bound on the non-trivial spectrum of the normalised adjacency operator of the non-bipartite Cayley graph $C(G,S)$.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relationAlso published in: Algebraic Combinatorics 4(2021), no. 3, pp. 517–531. https://doi.org/10.5802/alco.166en_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,21
dc.subjectExpander graphsen_US
dc.subjectCheeger inequalityen_US
dc.subjectSpectra of Cayley sum graphsen_US
dc.titleA Cheeger Type Inequality in Finite Cayley Sum Graphsen_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-2019-21
local.scientificprogramOWLF 2019en_US
local.series.idOWP-2019-21en_US
local.subject.msc05en_US
dc.identifier.urnurn:nbn:de:101:1-2019082215000890903293
local.date-range5 May - 27 July 2019en_US
dc.identifier.ppn1672110904


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