Journal ArticleDOI
The minimal Laplacian spectral radius of trees with given matching number
TLDR
In this paper, the set of trees on vertices with fixed matching number is determined, where is an integer greater than one i.e. a conjecture posed by Feng et al. is proved.Abstract:
Let denote the set of trees on vertices with fixed matching number . In this paper, the tree with minimal Laplacian spectral radius over is determined, where is an integer greater than one i.e. a conjecture posed by Feng et al. is proved (see [Feng LH, Li Q, Zhang XD. Minimizing the Laplacian spectral radius of trees with given matching number. Linear and Multilinear Algebra. 2007;55:199–207]).read more
Citations
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Proceedings ArticleDOI
Mining maximum matchings of controllability of directed networks based on in-degree priority
Yunyun Yang,Gang Xie +1 more
TL;DR: An algorithm is proposed to obtain maximum matchings of directed complex networks and enables effectively eliminating the transformation process of its bipartite equivalent graphs.
Journal ArticleDOI
Matchings in graphs from the spectral radius
TL;DR: In this article , it was shown that for a positive integer , if G is an n-vertex connected graph with the spectral radius, then the matching number of G, written , is the size of a maximum matching in G.
Journal ArticleDOI
Maximum Matchings of a Digraph Based on the Largest Geometric Multiplicity
Yunyun Yang,Gang Xie +1 more
TL;DR: For a given digraph, it has been proved that the number of maximum matched nodes has close relationship with the largest geometric multiplicity of the transpose of the adjacency matrix and through fundamental column transformations, the matched nodes and related matching edges are obtained.
Posted Content
A spectral extremal problem on graphs with given size and matching number
TL;DR: In this article, the authors considered the Brualdi-Hoffman type problem of graphs with given matching number and obtained the maximal $Q$-spectral radius of graph with given size and matching number.
Journal ArticleDOI
An extremal problem on Q-spectral radii of graphs with given size and matching number
TL;DR: Brualdi and Hoffman as mentioned in this paper proposed the problem of determining the maximal spectral radius of graphs with a given size, and showed that the problem is NP-hard and that the spectral radius can be computed in polynomial time.
References
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Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Journal ArticleDOI
Graph theory with applications (revised edition), by J. A. Bondy and U.S.R. Murty. Pp x, 264. £5·95 paperback. 1977. SBN 0 333 22694 1 (Macmillan)
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.
Journal ArticleDOI
The Laplacian spectrum of a graph
TL;DR: In this paper, the Laplacian matrix of a graph G = D(G) - A(G), where G is a graph and A is the adjacency matrix of vertices, is investigated.