The Spectral Radius of Graphs on Surfaces
Mark N. Ellingham,Xiaoya Zha +1 more
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New upper bounds on the spectral radius ?About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 2000-01-01 and is currently open access. It has received 72 citations till now. The article focuses on the topics: Adjacency matrix & Spectral radius.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
A Sharp Upper Bound of the Spectral Radius of Graphs
Yuan Hong,Jinlong Shu,Kunfu Fang +2 more
TL;DR: The following sharp upper bound is obtained of the minimum degree of vertices of G, which is either a regular graph or a bidegreed graph in which each vertex is of degree either ? or n?1.
Journal ArticleDOI
On the two largest Q-eigenvalues of graphs
TL;DR: In this paper, an upper bound for the largest signless Laplacian eigenvalue of a graph is given and all the extremal graphs are found and the well-known friendship graph is proved to be determined by the signlessLaPlacian spectrum.
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Three conjectures in extremal spectral graph theory
Michael Tait,Josh Tobin +1 more
TL;DR: This work uses the leading eigenvector of a purported extremal graph to deduce structural properties about that graph and proves three conjectures regarding the maximization of spectral invariants over certain families of graphs.
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On the Laplacian spectral radius of a graph
Huiqing Liu,Mei Lu,Feng Tian +2 more
TL;DR: In this article, an upper bound for the Laplacian spectral radius of the Nordhaus-Gaddum type of bipartite graphs was shown, where the minimum degree and the maximum degree of vertices of a simple graph are the minimum and maximum degrees of the vertices, respectively.
References
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Journal ArticleDOI
Encyclopedia of Mathematics and its Applications.
William B. Jones,W. J. Thron +1 more
Book
Eigenspaces of graphs
TL;DR: In this paper, the background in graph spectra is described as a background of a graph, and the graph angles and angles of graphs are modeled as Eigenvectors of graphs.
Journal ArticleDOI
The largest eigenvalue of a graph: A survey
Dragoš Cvetković,Peter Rowlinson +1 more
TL;DR: A survey of results concerning the largest eigenvalue (or index) of a graph can be found in this paper, where inequalities of the index, graphs with bounded index, ordering graphs by their indices, graph operations and modifications, random graphs, and applications.
Journal ArticleDOI
A bound on the spectral radius of graphs
Hong Yuan,Hong Yuan +1 more
TL;DR: In this paper, the spectral radius ϱ(A) of a simple connected graph with n vertices and m edges is defined as the adjacency matrix of the graph G and A is a matrix whose spectral radius is equal to 2m − n + 1 with equality if and only if G is isomorphic to one of the following two graphs: (a) the star K1,n−1; (b) the complete graph Kn.