A lower bound on the spectral radius of the universal cover of a graph
Reads0
Chats0
TLDR
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
Citations
More filters
Journal ArticleDOI
Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines
TL;DR: In this article, it was shown that the spectral radius of a graph can be defined by a finite set of forbidden subgraphs if and only if λ < λ √ 2.058.
Journal ArticleDOI
A strengthening and a multipartite generalization of the Alon-Boppana-Serre Theorem
TL;DR: In this article, a multipartite version of the Alon-Boppana-Serre theorem for graphs with bounded global girth was shown to be equivalent to the negative eigenvalues.
Journal ArticleDOI
A strengthening and a multipartite generalization of the Alon-Boppana-Serre theorem
TL;DR: In this paper, a multipartite version of the Alon-Boppana-Serre theorem for graphs of minimum degree and bounded maximum degree was shown to hold for non-regular graphs.
Journal ArticleDOI
Eigenvalues of graphs and a simple proof of a theorem of Greenberg
TL;DR: In this paper, it was shown that the same result holds for the smallest eigenvalues of the universal cover of a finite graph X ∈ {0, 1, 2}.
Posted Content
Spectra of infinite graphs via freeness with amalgamation
TL;DR: In this article, the authors use tools from free probability to study the spectra of certain operators on infinite graphs, including the adjacency operator and the Laplacian, and derive a new formula for the spectral radius of a universal cover.
References
More filters
Journal ArticleDOI
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.
Book
Discrete Groups, Expanding Graphs and Invariant Measures
TL;DR: The Banach-Ruziewicz Problem for n = 2, 3 Ramanujan Graphs is solved and the representation theory of PGL 2 is explained.
Journal ArticleDOI
Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q
TL;DR: For any prime power q, explicit constructions for many infinite linear families of q + 1 regular Ramanujan graphs are given as Cayley graphs of PGL2 or PSL2 over finite fields, with respect to very simple generators.
Journal ArticleDOI
On the second eigenvalue of a graph
TL;DR: In this paper, it was shown that the second largest eigenvalue of the adjacency matrix of any d-regular graph G containing two edges is at least 2 d − 1 − (2 d−1 − 1)/(k+1).
Journal Article
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.