It is proved that the Green’s function of the simple random walk on a surface group of large genus decays exponentially in distance at the (inverse) spectral radius. It is also shown that Ancona’s inequalities extend to the spectral radius R, and therefore that the Martin boundary for R−potentials coincides with the natural geometric boundary S. This implies that the Green’s function obeys a po...

We study the spectral radius of graphs with n vertices and k cut edges. In this paper, we show that of all the connected graphs with n vertices and k cut edges, the maximal spectral radius is obtained uniquely at Kk n , where K k n is a graph obtained by joining k independent vertices to one vertex of Kn−k . We also discuss the limit point of the maximal spectral radius. © 2004 Elsevier Inc. Al...

We introduce a new spectral method for the retrieval of optical thickness and effective radius from cloud transmittance that relies on the spectral slope of the normalized transmittance between 1565 nm and 1634 nm, and on cloud transmittance at a visible wavelength. The standard dual-wavelength technique, which is traditionally used in reflectance-based retrievals, is ill-suited for transmittan...

In 1962, Erdős gave a sufficient condition for Hamilton cycles in terms of the vertex number, edge number, and minimum degree of graphs which generalized Ore’s theorem. One year later, Moon and Moser gave an analogous result for Hamilton cycles in balanced bipartite graphs. In this paper we present the spectral analogues of Erdős’ theorem and Moon-Moser’s theorem, respectively. Let Gk n be the ...

In this paper we use preferred and quasi-preferred bases of generalized eigenspaces associated with the spectral radius of nonnegative matrices to analyze the existence and uniqueness of a variant of the Jordan canonical form which we call FrobeniusJordan form. It is a combination of the classical Jordan canonical form in the part associated with the eigenvalues that are different from the spec...

The spectral radius of the adjacency matrix can impact both algorithmic efficiency as well as the stability of solutions to an underlying dynamical process. Although much research has considered the distribution of the spectral radius for undirected random graph models, as symmetric adjacency matrices are amenable to spectral analysis, very little work has focused on directed graphs. Consequent...

In this paper, we show the evaluation of the spectral radius for node degree as the basis to analyze the variation in the node degrees during the evolution of scale-free networks and small-world networks. Spectral radius is the principal eigenvalue of the adjacency matrix of a network graph and spectral radius ratio for node degree is the ratio of the spectral radius and the average node degree...

We provide upper estimates on the spectral radius of a directed graph. In particular we prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.