Journal ArticleDOI
Spectral ordering of trees with small index
TLDR
In this article, the authors consider trees with index in the real interval (2, 2 + 5 ) and their ordering with respect to the index, and obtain the first 8 trees of even order with largest index.About:
This article is published in Linear Algebra and its Applications.The article was published on 2019-08-15. It has received 9 citations till now. The article focuses on the topics: Adjacency matrix & Spectral graph theory.read more
Citations
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Journal ArticleDOI
Most Laplacian eigenvalues of a tree are small
TL;DR: It is shown that the number of Laplacian eigenvalues greater than the average degree of a tree having $n$ vertices is at most $\lfloor\frac{n}{2} \rfloor$.
Posted Content
Most Laplacian eigenvalues of a tree are small
TL;DR: In this article, it was shown that the number of Laplacian eigenvalues greater than the average degree of a tree having n vertices is at most Ω(n 1/2 )
Journal ArticleDOI
Applications of rational difference equations to spectral graph theory
TL;DR: In this article, a general class of recurrence relations appeared in the application of matrix diagonalization procedure and they were studied in several problems involving eigenvalues of graphs, and the results of these relations were applied to several graph problems.
Journal ArticleDOI
Applications of rational difference equations to spectral graph theory
TL;DR: In this article, a general class of recurrence relations that appear in the application of a matrix diagonalization procedure are studied and a general closed formula and analytical properties of these relations are determined.
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Spectral ordering and 2-switch transformations
TL;DR: In this article, the problem of ordering trees with the same degree sequence by their spectral radii is addressed, and the main contribution is to determine a total ordering of a particular family by their indices according to a given parameter related to sizes in the tree.
References
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Book
Spectra of graphs : theory and application
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
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.
Book
Spectral Radius of Graphs
TL;DR: Graphs are naturally associated with matrices, as matrices provide a simple way of representing graphs in computer memory, and entries of the principal eigenvector of adjacency matrices have been used in the study of complex networks.
Related Papers (5)
Some extremal ratios of the distance and subtree problems in binary trees
Shuchao Li,Hua Wang,Shujing Wang +2 more