The spectral radius and the maximum degree of irregular graphs

Details The spectral radius and the maximum degree of irregular graphs The spectral radius and the maximum degree of irregular graphs

2007-02-22

arxiv.org/abs/math/0702627v1

Mathematics

Combinatorics

10 pages, 1 figure, submitted to EJC on January 20, 2007

Scientific paper

Let $G$ be an irregular graph on $n$ vertices with maximum degree $\Delta$
and diameter $D$. We show that \Delta-\lambda_1>\frac{1}{nD} where $\lambda_1$
is the largest eigenvalue of the adjacency matrix of $G$. We also study the
effect of adding or removing few edges on the spectral radius of a regular
graph.

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