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Distance-regular graphs with a few q-distance eigenvalues

Discrete Mathematics
Comment: 15 ...
Abdullah, Mamoon, Gebremichel, Brhane, Hayat, Sakander, Koolen, Jack H.   +3 more
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Remoteness and distance eigenvalues of a graph

Discrete Applied Mathematics, 2016
Let $G$ be a connected graph of order $n$ with diameter $d$. Remoteness $ $ of $G$ is the maximum average distance from a vertex to all others and $\partial_1\geq\cdots\geq \partial_n$ are the distance eigenvalues of $G$. In \cite{AH}, Aouchiche and Hansen conjectured that $ +\partial_3>0$ when $d\geq 3$ and $ +\partial_{\lfloor\frac{7d}{8 ...
Lin, Huiqiu, Das, Kinkar Ch., Wu, Baoyindureng   +2 more
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Average distance in graphs and eigenvalues

Discrete Mathematics, 2009
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Distance-regular graphs with small number of distinct distance eigenvalues

Linear Algebra and its Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdullah Alazemi, Milica Anđelić, Tamara Koledin, Zoran Stanić   +3 more
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Spectral properties of distance matrices [PDF]

, 2003
Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive.
Bogomolny E, C Schmit, Derrida B, E Bogomolny, Erdélyi A (ed), Gantmacher F R, Kac M, Lifshits I M, Mehta M L, O Bohigas, Schoenberg I J, Vershik A M   +11 more
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Tunneling between corners for Robin Laplacians [PDF]

, 2014
We study the Robin Laplacian in a domain with two corners of the same opening, and we calculate the asymptotics of the two lowest eigenvalues as the distance between the corners increases to infinity.Comment: 27 pages, 5 ...
Helffer, Bernard, Pankrashkin, Konstantin   +1 more
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The Generalized Distance Spectrum of the Join of Graphs [PDF]

, 2020
Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) .
Alhevaz, Abdollah, Baghipur, Maryam, Ganie, Hilal A., Shang, Yilun   +3 more
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Minimum Length from First Principles [PDF]

, 2005
We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that ...
Calmet, Xavier, Graesser, Michael, Hsu, Stephen D. H.   +2 more
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Locally Testable Codes and Cayley Graphs [PDF]

, 2013
We give two new characterizations of ($\F_2$-linear) locally testable error-correcting codes in terms of Cayley graphs over $\F_2^h$: \begin{enumerate} \item A locally testable code is equivalent to a Cayley graph over $\F_2^h$ whose set of generators ...
Ben-Sasson Eli, Biggs Norman, Goldreich Oded, Lee James, Matousek Jiri, Viderman Michael   +5 more
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Eigenvalues of Euclidean distance matrices

Journal of Approximation Theory, 1992
Let \(x_ 1,x_ 2,\dots,x_ n\) be \(n\) points (\(n>1\)) in \(R^ d\) with \(\| x_ i-x_ j\|\geq\varepsilon\) for \(i\neq j\). It is proved that the matrix \(A=(\| x_ i-x_ j\|)_{i,j=1,\dots,n}\) has an inverse \(A^{-1}\), whose norm (as an operator on \(\ell^ n_ 2\)) verifies the inequality \(\| A^{-1}\|\leq c\sqrt{d}/\varepsilon\), where \(c\) is an ...
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