Lower estimates on eigenvalues of quantum graphs

On the distance eigenvalues of Cayley graphs

In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...

On the eigenvalues of non-commuting graphs

The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

Tight estimates for eigenvalues of regular graphs

It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2 √ d − 1 cos( π 2k ). A similar result has been proved by Friedman using more sophisticated tools.

Quantum Walks on Regular Graphs and Eigenvalues

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S+(U3), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of S+(U) and S+(U2) for regular graphs and show that S+(U2) = S+(U)2 + I.

Tight Estimates for Eigenvalues of Regular Graphs