Related papers: Walks and the spectral radius of graphs
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
The generalized distance spectral radius of a connected graph $G$ is the spectral radius of the generalized distance matrix of $G$, defined by $$D_\alpha(G)=\alpha Tr(G)+(1-\alpha)D(G), \;\;0\le\alpha \le 1,$$ where $D(G)$ and $Tr(G)$…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every…
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This…
We characterise the form of all simple, finite graphs for which the girth of the graph is equal to the circumference of the graph. We apply this to prove a bound on the number of edges in such a graph.
It is well known that the spectral radius of a tree whose maximum degree is $D$ cannot exceed $2\sqrt{D-1}$. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of bounded genus. It is proved that a the…
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs.…
In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral…
We provide lower bounds on the gonality of a graph in terms of its spectral and edge expansion. As a consequence, we see that the gonality of a random 3-regular graph is asymptotically almost surely greater than one seventh its genus.
We consider random walks on edge coloured random graphs, where the colour of an edge reflects the cost of using it. In the simplest instance, the edges are coloured red or blue. Blue edges are free to use, whereas red edges incur a unit…
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…
There are a lot of recent works on generalizing the spectral theory of graphs and graph partitioning to hypergraphs. There have been two broad directions toward this goal. One generalizes the notion of graph conductance to hypergraph…
We examine the stationary distribution of random walks on directed graphs. In particular, we focus on the {\em principal ratio}, which is the ratio of maximum to minimum values of vertices in the stationary distribution. We give an upper…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.