Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
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01 May 2018
TL;DR: This paper describes a method to find a graph partition when, due to limited jammer range, the authors cannot affect all the links in the network, but the links are all known.
Abstract: Knowing the topology of an adversarial network, heuristics exist based on spectral graph theory for calculating which edges, when removed, will partition the network. Knowing these weak links in the network under attack, a surgical jammer may be used to conduct man-in-the-middle attacks or to maximally affect the adversary network's connectivity. However, it is not always possible to control where the jammer is located with respect to the network. This paper describes a method to find a graph partition when, due to limited jammer range, we cannot affect all the links in the network, but the links are all known.
2 citations
TL;DR: In this article, a new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching.
Abstract: Abstract A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching. Furthermore, computational experiments revealed that the introduced lower bound is better than the known ones. The paper also gives sufficient condition for a graph to be non Hamiltonian (or without a perfect matching).
2 citations
19 Dec 1997
TL;DR: In this paper, a newa priori estimate for very weak p{harmonic mappings when pis close to two is given, which sheds some light on a conjecture posed by Iwaniec and Sbordone.
Abstract: We prove a newa priori estimate for very weak p{harmonic mappings when pis close to two. This sheds some light on a conjecture posed by Iwaniec and Sbordone.
2 citations
Posted Content•
TL;DR: This work introduces a novel formulation for geometry on discrete points based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions and works on spectral graph theory and random walks.
Abstract: We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so that it is consistent with differential geometry, and works on spectral graph theory and random walks. Consequently, our formulation comprehensively demonstrates many discrete frameworks in probability theory, physics, applied harmonic analysis, and machine learning. Our approach would suggest the existence of an intrinsic theory and a unified picture of those discrete frameworks.
2 citations
2 citations