Silvery radioactive metallic element is known as actinium. Due to its high radioactivity and blue light, actinium glows in the dark. A recent discipline of applied chemistry is chemical graph theory. A topological index is a numerical value that links the thermodynamic properties of a chemical structure. Due to the importance of this structure, we computed the topological indices such as Randic, Zagreb Indices and so on. In this paper, we calculate topological indices of actinium(III) fluoride. A few degree-based entropies are computed from topological indices. Additionally, a connection has been made between the thermodynamic features of actinium(III) fluoride and Shannon entropy. The numerical and graphical representations of the computed data were combined with curve fitting between the calculated information entropies and the heat of formation.