Energy of zero-divisor graphs via distance-based fuzzy adjacency matrices

In this paper, we investigate the energy of zero-divisor graphs of finite commutative rings with unity using the distance-based fuzzy adjacency matrix. In view of this, first we characterize the rings whose zero-divisor graphs have energy zero and then prove that the energy of a zero-divisor graph can never equal $1$. Further we establish the sharp bounds for energy of zero-divisor graphs and characterize the rings $R$ for which energy attains the value $2$.