dc.contributor.author Biswas, Arindam dc.contributor.author Saha, Jyoti Prakash dc.date.accessioned 2019-07-31T06:18:57Z dc.date.available 2019-07-31T06:18:57Z dc.date.issued 2019-07-31 dc.identifier.uri http://publications.mfo.de/handle/mfo/2512 dc.description.abstract Let $G$ 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.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2019,21 dc.subject Expander graphs en_US dc.subject Cheeger inequality en_US dc.subject Spectra of Cayley sum graphs en_US dc.title A Cheeger Type Inequality in Finite Cayley Sum Graphs en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2019-21 local.scientificprogram OWLF 2019 en_US local.series.id OWP-2019-21 en_US local.subject.msc 05 en_US local.date-range 5 May - 27 July 2019 en_US
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