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Showing papers on "Spectral graph theory published in 1996"


Book
03 Dec 1996
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
Abstract: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigenvalues and quasi-randomness Expanders and explicit constructions Eigenvalues of symmetrical graphs Eigenvalues of subgraphs with boundary conditions Harnack inequalities Heat kernels Sobolev inequalities Advanced techniques for random walks on graphs Bibliography Index.

6,948 citations


Journal ArticleDOI
TL;DR: Formulas are given to express the Laplacian polynomial and the number of spanning trees of a threshold graph in terms of its degree sequence, and threshold graphs are shown to be uniquely defined by their spectrum.

65 citations




Journal ArticleDOI
TL;DR: In this article, it was shown that the spectral moment of a polymeric graph composed of n monomer units is an exact linear function of the parametern, and that this linear relation holds for all values of n, greater than a critical value ξ 0=ξ 0(k).
Abstract: It is shown that for anyk, thekth spectral moment of a polymer graph composed ofn monomer units is an exact linear function of the parametern. This linear relation holds for all values ofn, greater than a critical value ξ0=ξ0(k).

16 citations


Book ChapterDOI
03 Dec 1996

11 citations


Journal ArticleDOI
TL;DR: In this article, the same techniques are applied to the problem of estimating eigenvalues of the adjacency operator on finite graphs of bounded degree, and they show that the largest eigenvalue on a finite graph Γ may be bounded in terms of the biggest eigen values on the geodesic balls in Γ.
Abstract: In this paper, we explore what happens when the same techniques are applied to the problem of estimating eigenvalues of the adjacency operator on finite graphs of bounded degree. In Theorem 7, we show how eigenvalues of the adjacency operator on a finite graph Γ may be bounded in terms of the biggest eigenvalues of the adjacency operator on “geodesic balls” in Γ. We find explicit bounds for the eigenvalues on the balls (Theorem 6), and in Theorem 8, we turn these into explicit estimates on certain eigenvalues of the adjacency operator on Γ.

9 citations