Related papers: Walks and the spectral radius of graphs

We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.

This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying…

We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…

We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

In this paper, we obtain two spectral upper bounds for the $k$-independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than $k$. We construct graphs that attain equality for our first…

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices…

It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n, p) converges to the semicircle law in case np tends to infinity with n. The spectral measure for random graphs G(n, c/n)…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

We give an upper bound on the largest eigenvalue of a graph of given order, size, and girth.

We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…

For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum of the absolute values of the eigenvalues of its distance matrix. We establish lower and…

We give a bound on the spectral radius of a graph implying a quantitative version of the Erdos-Stone theorem.

The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a graph and $t$ is a sufficiently small positive…

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…

In this paper, we will construct formulas and bounds for Neighborhood Degree-based indices of graphs and describe graphs that attain the bounds. Furthermore, we will establish a lower bound for the spectral radius of any graph.

We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…

This paper presents a sharp upper bound for the spectral radius of simple digraphs with described number of arcs. Further, the extremal graphs which attain the maximum spectral radius among all simple digraphs with fixed arcs are…