Geodesic
The spectral radius and the maximum degree of irregular graphs
The electronic journal of combinatorics, Tome 14 (2007)
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Let $G$ be an irregular graph on $n$ vertices with maximum degree $\Delta$ and diameter $D$. We show that $$ \Delta-\lambda_1>{1\over nD}, $$ 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.
DOI : 10.37236/956
Classification : 05C50, 15A18 
@article{10_37236_956,
     author = {Sebastian M. Cioab\u{a}},
     title = {The spectral radius and the maximum degree of irregular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/956},
     zbl = {1122.05056},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/956/}
}
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Sebastian M. Cioabă. The spectral radius and the maximum degree of irregular graphs. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/956

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