Brualdi, Richard A.; Solheid, Ernie S. On the spectral radius of connected graphs. (English) Zbl 0603.05028 Publ. Inst. Math., Nouv. Sér. 39(53), 45-54 (1986). 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 Cited in 61 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C35 Extremal problems in graph theory Keywords:sepctral radius PDFBibTeX XMLCite \textit{R. A. Brualdi} and \textit{E. S. Solheid}, Publ. Inst. Math., Nouv. Sér. 39(53), 45--54 (1986; Zbl 0603.05028) Full Text: EuDML