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On the spectral radius of connected graphs. (English) Zbl 0603.05028

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. The authors determine connected graphs with n vertices and e edges with maximum spectral radius when \(e=n+s\) (0\(\leq s\leq 5)\) and n sufficiently large. These graphs consist of pendant edges attached at a vertex of maximal degree of \(G_ s\) where \(G_ s\) in \(K_ 3\), \(K_ 4- e\), \(K_ 4\) for \(s=0,1,2\) and \(\overline{K_ s\cup 2K_ 1}\) for \(s=3,4,5\).
Reviewer: D.Cvetkovic

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C35 Extremal problems in graph theory

Keywords:

sepctral radius
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