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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