Stability and Maximum Independent Bond Set Polynomials of Painkiller Molecules Using Maximum Matching

Chemical graph theory establishes a connection between the properties of molecules and their corresponding molecular graphs. A topological index is a graph invariant that characterizes the graph's structure and remains unaffected by graph automorphisms. In chemical graph theory, degree-based topological indices are particularly significant, offering crucial insights into the structural features of molecules. In this work, we introduce the maximum independent bond set polynomial $MIBSP(H;x,y)$, a powerful tool for deriving various degree-based topological indices. We specifically apply $MIBSP(H;x,y)$, to the chemical graphs of several painkiller molecules, including Aspirin, Paracetamol, Caffeine, Ibuprofen, Phenacetin, and Salicylic acid. The degree-based topological indices derived from these polynomials provide a deeper understanding of the molecular structures and their potential applications in pharmaceutical research.