Conjectured bounds for the sum of squares of positive eigenvalues of a graph

Clive Elphick, Felix Goldberg, Miriam Farber +1

A well known upper bound for the spectral radius of a graph, due to Hong, is that ${\mu }_1^2\le 2m-n+1$. It is conjectured that for connected graphs $n-1\le s^{+}\le 2m-n+1$…