Computation of differential and integral operators using M -polynomials of gold crystal

Gold is generally considered a noble metal since it is inherently inert in its bulk state. However, gold demonstrates reactivity when it is in its ionic state. The inherent inertness of bulk gold has resulted in its widespread recognition as a vital raw material in various biomedical processes. The applications of these technologies include drug delivery microchips, dental prostheses, reconstructive surgery, culinary additives, and cardiovascular stents. Gold can also exist in molecules or ions, particularly gold ions, which facilitates the production of gold nanomaterials. In this paper, we have computed differential and integral operators by using the $M$ -Polynomial of gold crystals and by utilizing this polynomial, we have also computed eleven topological indices like $1^{st}$ Zagreb, $2^{nd}$ Zagreb, Hyper, Sigma, Second Modified, General Randic, General Reciprocal Randic, $3^{rd}$ Redefined Zagreb, Symmetric Division Degree, Harmonic, Inverse Sum indices for the structure of Gold crystal.