Elsevier, Discrete Applied Mathematics, 10(156), p. 1670-1682, 2008
DOI: 10.1016/j.dam.2007.08.027
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The index of a graph is the largest eigenvalue (or spectral radius) of its adjacency matrix. We consider the problem of ordering graphs by the index in the class of connected graphs with a fixed order n and index belonging to the interval (2,√(2+√5)). For any fixed n (provided that n is not too small), we order a significant portion of graphs whose indices are close to the end points of the above interval.