Positive and negative square energies of graphs

The energy of a graph $G$ is the sum absolute values eigenvalues adjacency matrix $G$. Let $s^+(G), s^-(G)$ denote squares positive and negative $G$, respectively. It was conjectured by [Elphick, Farber, Goldberg, Wocjan, Discrete Math. (2016)] that if connected order $n$, then $s^+(G)\geq n-1$ $s^-(G) \geq n-1$. In this paper, we show partial results towards conjecture. particular, numerous structural may help in proving conjecture are derived, including effect various operations. These used to establish for several classes, graphs with certain fraction unicyclic graphs.