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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TL;DR: It is proved that the sum of k largest eigenvalues of G is at most 12(k+1)n and this bound is shown to be best possible in the sense that for every k there exist graphs whose sum is 12( k+12)n-o(k^-^2^/^5)n.
20 citations
TL;DR: Some new and improved sharp upper bounds on the spectral radius q"1(G) of the signless Laplacian matrix of a graph G are obtained.
20 citations
TL;DR: This paper proposes a novel non-parametric technique for clustering networks based on their structure to rely on two ways to project a weighted form of the eigenvalues of a graph into a low-dimensional space.
20 citations
TL;DR: The proposed method for learning graph affinities for salient object detection has an insignificant computational burden on, but significantly outperforms the baseline EQCut and achieves a comparable performance level with the state-of-the-art in some performance measures.
20 citations
TL;DR: In this article, the characteristic polynomial, the admittance (or Laplacian) polynomials and the matching polynomorphism of a connected antiregular graph are studied.
Abstract: An antiregular graph is a simple graph with the maximum number of vertices with different degrees. In this paper we study the characteristic polynomial, the admittance (or Laplacian) polynomial and the matching polynomial of a connected antiregular graph. For these polynomials we obtain recurrences and explicit formulas. We also obtain some spectral properties. In particular, we prove an interlacing property for the eigenvalues and we give some bounds for the energy.
20 citations