This is a new contribution to the question: Can we see from the spectrum of a graph whether it is distance-regular? By generalizing some results of Van Dam and Haemers, among others, we give some new spectral and quasi-spectral characterizations of distance-regularity. In this area of research, typical results concluding that a graph is distance regular require that G is cospectral with a dista...

Distance is a fundamental concept in spatial sciences. Spatial distance is a very important parameter to measure the relative positions between spatial objects and to indicate the degree of similarity between neighbouring objects. Indeed, spatial distance plays an important role in spatial query, analysis and reasoning. However, how to represent directional relations in a unified form is still ...

A general formula for the asymptotic largest minimum distance (in block length) of deterministic block codes under generalized distance functions (not necessarily additive, symmetric, and bounded) is presented. As revealed in the formula, the largest minimum distance can be fully determined by the ultimate statistical characteristics of the normalized distance function evaluated under a properl...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

The D-eigenvalues {μ1, μ2, . . . , μn} of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G) . The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there ex...

The distance matrix of a simple connected graph G is D(G) = (dij), where dij is the distance between ith and jth vertices of G. The multiset of all eigenvalues of D(G) is known as the distance spectrum of G. Lin et al.(On the distance spectrum of graphs. Linear Algebra Appl., 439:1662-1669, 2013) asked for existence of graphs other than strongly regular graphs and some complete k-partite graphs...

This paper starts by considering the minimization of the Rényi divergence subject to a constraint on the total variation distance. Based on the solution of this optimization problem, the exact locus of the points ( D(Q∥P1), D(Q∥P2) ) is determined when P1, P2, Q are arbitrary probability measures which are mutually absolutely continuous, and the total variation distance between P1 and P2 is not...

An exact information spectrum-type formula for the maximum size of finite length block codes subject to a minimum pairwise distance constraint is presented. This formula can be applied to codes for a broad class of distance measures. As revealed by the formula, the largest code size is fully characterized by the information spectrum of the distance between two independent and identically distri...

Distance adaptive spectrum allocation exploits the tradeoff between spectrum width and reach to improve resource utilisation by tailoring the modulation format to the level of impairments along the path. The authors first show that the distance-adaptive routing and spectrum assignment (DA-RSA) problem is a special case of a multiprocessor scheduling problem. The authors then develop a suite of ...

The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many of the commonly studied spectra of graphs. We show that for a large class of graphs these eigenvalues can be computed explicitly. We also present the applicat...