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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.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.identifier.doi10.14760/OWP-2019-21
local.scientificprogramOWLF 2019en_US
local.series.idOWP-2019-21en_US
local.subject.msc05en_US
local.date-range5 May - 27 July 2019en_US


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