相关论文: Walks and the spectral radius of graphs

We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…

We are interested in the general question: to what extent are the spectral properties of a graph connected to the distance function? Our motivation is a concrete example of this question that is due to Steinerberger. We provide some…

This paper gives the quantum walks determined by graph zeta functions. The result enables us to obtain the characteristic polynomial of the transition matrix of the quantum walk, and it determines the behavior of the quantum walk. We treat…

Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be the diagonal matrix of the degrees of $G$. For every real $\alpha\in\left[ 0,1\right] $, write $A_{\alpha}\left( G\right) $ for the matrix \[ A_{\alpha}\left( G\right)…

Let $G$ be a graph with adjacency matrix $A(G)$, and let $D(G)$ be the diagonal matrix of the degrees of $G$. For any real $\alpha\in[0,1]$, write $A_\alpha(G)$ for the matrix $$A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G).$$ This paper presents…

We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first…

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…

We study topological properties of the graph topology.

We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…

Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. In the present paper, we develop a spectral analysis for lamplighter random…

Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…

For a finite simple graph $G$ we give an upper bound for the regularity of the powers of the edge ideal $I(G)$.

We present lower and upper bounds for the geometric-arithmetic index of unicyclic graphs and provide extremal graphs for the corresponding bounds.

Two method for computation of the spectra of certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on the spectral theory of Jacobi matrices. The second…

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of…

A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…

Characterizations graphs of some classes to induce periodic Grover walks have been studied for recent years. In particular, for the strongly regular graphs, it has been known that there are only three kinds of such graphs. Here, we focus on…

We investigate numerically the scattering of waves on discrete graphs. An efficient algorithm is developed to compute the reflection and transmission (spectral) coefficients. We then explore various configurations of input and output leads,…

Given a graph G of order n and size m, let s(G)= sum|d(u)-2m/n|, where the sum is taken over all vertices u of G. We investigate upper and lower bounds on eigenvalues of G in terms of s(G).

We give upper bounds on the order of the automorphism group of a simple graph