Maximizing signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity

In this paper, we characterize the graphs with maximum signless Laplacian or adjacency spectral radius among all graphs with fixed order and given vertex or edge connectivity. We also discuss the minimum signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity. Consequ...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 433; no. 6; pp. 1180 - 1186
Main Authors: Ye, Miao-Lin, Fan, Yi-Zheng, Wang, Hai-Feng
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.11.2010
Elsevier
Subjects:
Adjacency matrix
Algebra
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Connectivity
Exact sciences and technology
Flows in networks. Combinatorial problems
Graph
Graph theory
Linear and multilinear algebra, matrix theory
Mathematics
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Signless Laplacian matrix
Spectral radius
Graph
Signless Laplacian matrix
05C50
Spectral radius
05C40
Adjacency matrix
Connectivity
90C27
Perron value
Graph theory
Combinatorial optimization
Laplacian
Upper bound
ISSN:0024-3795
Online Access:Get full text
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Summary:In this paper, we characterize the graphs with maximum signless Laplacian or adjacency spectral radius among all graphs with fixed order and given vertex or edge connectivity. We also discuss the minimum signless Laplacian or adjacency spectral radius of graphs subject to fixed connectivity. Consequently we give an upper bound of signless Laplacian or adjacency spectral radius of graphs in terms of connectivity. In addition we confirm a conjecture of Aouchiche and Hansen involving adjacency spectral radius and connectivity.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.04.045