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Zbl 0603.05028
Brualdi, Richard A.; Solheid, Ernie S.
On the spectral radius of connected graphs.
(English)
[J] Publ. Inst. Math., Nouv. Sér. 39(53), 45-54 (1986). ISSN 0350-1302

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$\le s\le 5)$ and n sufficiently large. These graphs consist of pendant edges attached at a vertex of maximal degree of $G\sb s$ where $G\sb s$ in $K\sb 3$, $K\sb 4- e$, $K\sb 4$ for $s=0,1,2$ and $\overline{K\sb s\cup 2K\sb 1}$ for $s=3,4,5$.
[D.Cvetkovic]
MSC 2000:
*05C50 Graphs and matrices
05C35 Extremal problems (graph theory)

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