Degree-Based Graph Entropy in Structure–Property Modeling

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose (Formula presented.) is degree of the vertex (Formula presented.) for each (Formula presented.). Now, the k-th degree-based graph entropy for G is defined as (Formula presented.) where k is real number. The first-degree-based entropy is generated for (Formula presented.), which has been well nurtured in last few years. As (Formula presented.) yields the well-known graph invariant first Zagreb index, the (Formula presented.) for (Formula presented.) is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of (Formula presented.) in structure property modeling of molecules.