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The spectral radii of a graph and its line graph

โœ Scribed by Lingsheng Shi

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
150 KB
Volume
422
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

The spectral radius of a (directed) graph is the largest eigenvalue of adjacency matrix of the (directed) graph. We give the relation on the characteristic polynomials of a directed graph and its line graph, and obtain sharp bounds on the spectral radius of directed graphs. We also give the relation on the spectral radii of a graph and its line graph. As a consequence, the spectral radius of a connected graph does not exceed that of its line graph except that the graph is a path.

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