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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the adjacency, Laplacian and incidence matrices for a quaternion unit gain graph were defined, and bounds for both the left and right eigenvalues of the adjACency matrix were derived for the cycle and path graphs.
8 citations
TL;DR: In this paper, an edge subdividing theorem for Laplacian eigenvalues of a graph was given and a class of k-cyclic graphs whose algebraic connectivity is less than one was characterized.
Abstract: A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra.
8 citations
Journal Article•
TL;DR: Some recent developments and several unsolved problems on the research of Laplacian graph eigenvalues are presented in this article, where the authors present a survey of the literature on graph eigens.
8 citations
TL;DR: It is shown that the spectral properties of the Maury matrix characterize the flow asymmetry in lung airway networks more concisely than the Laplacian modes, and that eigenvector centrality in theMaury spectrum is closely related to the phenomenon of ventilation heterogeneity caused by airway narrowing or obstruction.
Abstract: This paper introduces a linear operator for the purposes of quantifying the spectral properties of transport within resistive trees, such as airflow in lung airway networks. The operator, which we ...
8 citations
TL;DR: In this paper, the authors give a simple arithmetic condition for a self-converse oriented graph being DGSS, which provides an analogue of a similar result for ordinary graphs; see [15].
8 citations