Geodesic
On $\lambda_{1}$-extremal non-regular graphs
The electronic journal of linear algebra, Tome 18 (2009), pp. 735-744.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let G be a connected non-regular graph with n vertices, maximum degree $\Delta $and minimum degree $\delta $, and let $\lambda 1$ be the greatest eigenvalue of the adjacency matrix of G. In this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not $\lambda 1$ -extremal graphs. Moreover, for each connected non-regular graph some lower bounds on the difference between $\Delta $and $\lambda 1$ are obtained.
Classification : 05C50, 15A48
Keywords: spectral radius, non-regular graph, lambda 
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Liu, Bolian; Huang, Yufei; You, Zhifu. On $\lambda_{1}$-extremal non-regular graphs. The electronic journal of linear algebra, Tome 18 (2009), pp. 735-744. http://geodesic.mathdoc.fr/item/ELA_2009__18__a5/