Spectra of Graphs

By Andries E. Brouwer, Willem H. Haemers. 2011

2,935 citations recorded by the source corpus.

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In Algorithms & Complexity

Citations in the corpus

Generalized Results for the Existence and Consistency of the MLE in the Bradley-Terry-Luce Model (2021, background): “It follows from Proposition 1.7.1 in Brouwer & Haemers (2011) that λ 2 ( (cid:101) L ) ≥ λ 2 ( L ) .”
On the sum of Laplacian eigenvalues of graphs (2010, neutral): “1]) and k > n− 1 (trivial), and (iv) for all graphs with at most ten vertices (by computer; see [3]).”
Skew-adjacency matrices of graphs (2012, methodology): “Linear Algebra and its Applications xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect Linear Algebra and its Applications journal homepage: www.elsevier .com/locate/ laa Skew-adjacency matrices of graphs M. Cavers a,1, S.M. Cioabă b,2, S. Fallat c,3, D.A. Gregory, d,∗,3, W.H. Ha”
Spectral Graph Theory (2012, background): “For those who want to learn more, the following books and survey papers take an approach in the spirit of this Chapter: [96, 97, 98, 81, 3, 40].”
ON THREE CONJECTURES INVOLVING THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS (2009, background): “For more information about the spectral radius of graphs, the reader can refer to [4].”
Spectra of the neighbourhood corona of two graphs (2012, background): “The A-spectrum of K p,q [1,3] consists of ±√pq with multiplicity one, and 0 with multiplicity p+q −2.”
H$^+$-Eigenvalues of Laplacian and Signless Laplacian Tensors (2013, background): “As in spectral graph theory [2], we may call eigenvalues (respectively, H-eigenvalue or H-eigenvalue or H-eigenvalue or spectrum or spectral radius) of A as eigenvalues (respectively, H-eigenvalue or H-eigenvalue or H-eigenvalue or spectrum or spectral radius) of the k-graph G, or simply eigenvalues”
Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae (2012, background): “Then the A-spectrum of G Kp,q consists of: (a) 0, repeated m+ (p+ q − 3)n times; (b) four roots of the equation x4 − [ pq + (1 + p+ q)(λj(G) + r) ] x2 − 2pq(λj(G) + r)x+ pq(λj(G) + r) = 0 for each j = 1, 2, . . . , n1.”
Eigenvector Statistics of Sparse Random Matrices (2016, background): “87. TheworkofH.-T.Y.ispartiallysupported by theNSFgrantDMS-1307444, DMS-1606305andaSimonsInvestigator award. 1 investigated for over half a century. To mention some, we refer the readers to the books [8,9] for a general discussion on spectral graph theory, the survey article [23] for the connection ”
On the normalized Laplacian energy and general Randić index R-1 of graphs (2010, background): “It is known that the adjacency matrix of G has only one positive eigenvalue if and only if G is a complete multipartite graph plus isolated vertices (see [5]).”
THE NORMALIZED LAPLACIAN MATRIX AND GENERAL RANDI C INDEX OF GRAPHS (2010, methodology): “Since then, spectral graph theory has been well documented in several surveys and books (for example, see [2, 3, 8, 16, 17, 18, 27, 60]).”
Some properties of the distance Laplacian eigenvalues of a graph (2013, background): “For more details about the adjacency spectrum of a graph see the books [5, 9, 10, 11, 24].”