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On the spectral radius of graphs. (English) Zbl 1041.05051

Summary: Let \(G\) be a simple undirected graph. For \(v \in V(G)\), the 2-degree of \(v\) is the sum of the degrees of the vertices adjacent to \(v\). Denote by \(\rho(G)\) and \(\mu(G)\) the spectral radius of the adjacency matrix and the Laplacian matrix of \(G\), respectively. In this paper, we present two lower bounds of \(\rho(G)\) and \(\mu(G)\) in terms of the degrees and the 2-degrees of vertices.

MSC:

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