Let $\eta_{ 1}\ge \eta_{ 2}\ge\cdots\ge \eta_{ n}$ be the eigenavalues of $\mathcal{ ABS}$ matrix. In this paper, we characterize connected graphs with $\mathcal{ ABS}$ eigenvalue $\eta_{ n}>-1$. As a result, we determine all connected graphs with exactly two distinct $\mathcal{ ABS}$ eigenvalues. We show that a connected bipartite graph has three distinct $\mathcal{ ABS}$ eigenvalues if and only if it is a complete bipartite graph. Furthermore, we present some bounds for the $\mathcal{ ABS}$ spectral radius (resp. $\mathcal{ ABS}$ energy) and characterize extremal graphs. Also, we obtain a relation between $\mathcal{ ABC}$ energy and $\mathcal{ ABS}$ energy. Finally, the chemical importance of $\mathcal{ ABS}$ energy is investigated and it shown that the $\mathcal{ ABS}$ energy is useful in predicting certain properties of molecules.
Categories: math.CO