Graphs with three distinct eigenvalues and largest eigenvalue less than 8
H. Chuang,Gholamreza Omidi +1 more
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In this paper, the authors consider graphs with three distinct eigenvalues and characterize those with the largest eigenvalue less than 8, and give an upper bound on the number of vertices of graphs with a given number of distinct Eigenvalues in terms of the largest Eigenvalue.About:
This article is published in Linear Algebra and its Applications.The article was published on 2009-04-15 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Eigenvalue perturbation & Divide-and-conquer eigenvalue algorithm.read more
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BookDOI
Spectra of graphs
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
Journal ArticleDOI
Equiangular lines in Euclidean spaces
TL;DR: A new general lower bound is presented on the maximum number of equiangular lines in d dimensional Euclidean space and the nonexistence of certain regular graphs with four eigenvalues is proved, as well as correcting some tables from the literature.
Journal ArticleDOI
On the distance spectrum of graphs
TL;DR: In this article, it was shown that the complete k-partite graph is determined by its D -spectrum, and that all connected graphs of diameter 2 have at least three D -eigenvalues when λ 1 (D ) is not an integer.
Journal ArticleDOI
Biregular graphs with three eigenvalues
TL;DR: The focus is mainly on the case of graphs having two distinct valencies and the results include constructions of new examples, structure theorems, valency constraints, and a classification of certain special families of such graphs.
Journal ArticleDOI
A note on graphs whose signless Laplacian has three distinct eigenvalues
TL;DR: In this paper, it was shown that the largest signless Laplacian eigenvalue of a connected graph with three distinct eigenvalues is noninteger if and only if G = K n ǫ−−ǫ for n ≥ 4, where K n is the n vertex complete graph with an edge removed.
References
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BookDOI
Spectra of graphs
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
Journal ArticleDOI
Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
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Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
Journal ArticleDOI
Line graphs, root systems, and elliptic geometry
TL;DR: In this paper, star-closed sets of lines at 60° and 90° are discussed, leading to a theorem that leaves only a restricted number of possibilities, of a specific structure.