A lower bound on the spectral radius of the universal cover of a graph
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It is proved that if the average degree of the graph G after deleting any radius r ≥ 2 ball is at least d ≥ 2, then its second largest eigenvalue in absolute value λ(G) is at at least 2 √d - 1(1 - c log r/r).About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 2005-01-01 and is currently open access. It has received 34 citations till now. The article focuses on the topics: Bound graph & Graph power.read more
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Phd by thesis
TL;DR: In this paper, a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) is presented.
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Expander graphs and their applications
S Hoory,Nathan Linial +1 more
TL;DR: Expander graphs were first defined by Bassalygo and Pinsker in the early 1970s, and their existence was proved in the late 1970s as discussed by the authors and early 1980s.
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On discrete groups
Young-Hyun Cho,Jae-Myung Chung +1 more
TL;DR: In this article, the authors define small submodules of a module M over R over a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E.
Posted Content
The Non-Backtracking Spectrum of the Universal Cover of a Graph
TL;DR: In this paper, it was shown that the spectral radius of the non-backtracking walk operator on the tree covering a finite graph is exactly Θ(n), where n is the growth rate of the tree.
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The non-backtracking spectrum of the universal cover of a graph
TL;DR: In this article, it was shown that the spectral radius of the non-backtracking walk operator on a tree covering a finite graph is exactly √ gr, where gr is the growth rate of the tree.
References
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Random walks, spectral radii, and Ramanujan graphs
TL;DR: In this paper, the authors investigate properties of random walks on trees with finitely many cone types and apply their results to get estimates on spectral radii of groups and to check whether a given finite graph is Ramanujan.