On the Laplacian spectral radii of bipartite graphs

The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we provide structural and behavioral details of graphs with maximum Laplacian spectral radius among all bipartite connected graphs of given order and size. Using these results, we pr...

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Bibliographic Details
Published in:Linear algebra and its applications 2011-11, Vol.435 (9), p.2183-2192
Main Authors: Li, Jianxi, Shiu, Wai Chee, Chan, Wai Hong
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Bipartite graph
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Exact sciences and technology
Graph theory
Information retrieval. Graph
Laplacian spectral radius
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Theoretical computing
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Summary:The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we provide structural and behavioral details of graphs with maximum Laplacian spectral radius among all bipartite connected graphs of given order and size. Using these results, we provide a unified approach to determine the graphs with maximum Laplacian spectral radii among all trees, and all bipartite unicyclic, bicyclic, tricyclic and quasi-tree graphs, respectively.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.04.008