On the maximal index of graphs with a prescribed number of edges
The index of a finite simple graph is the largest eigenvalue of its (0,1)-adjacency matrix. In the paper the author answers in the affirmative a conjecture of Brualdi and Hoffman, namely he shows that the maximal index among all graphs with n edges is attained by the graph obtained from the complete graph on d vertices, \({d\choose 2}<n<{d+1\choose 2}\), by adding one new vertex of degree \(n-{d\choose 2}\).
scientific article; zbMATH DE number 4089587