Sharp upper bounds on the spectral radius of graphs. (English) Zbl 1030.05073

Shu, Jinlong; Wu, Yarong

Linear Algebra Appl. 377, 241-248 (2004).

Summary: Let \(G\) be a simple connected graph with \(n\) vertices, \(m\) edges and degree sequence \(d_1 \geqslant d_2 \geqslant \cdots \geqslant d_n\). The spectral radius \(\rho(G)\) of graph \(G\) is the largest eigenvalue of its adjacency matrix. In this paper, we present some sharp upper bounds of the spectral radius in terms of the degree sequence of graphs.

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C07	Vertex degrees

Keywords:

Spectral radius; Upper bound; Largest degree; Similar matrices; degree sequence

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