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 be a graph of order . Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n. Now, the -th degree-based graph entropy for is defined as Id,k(G)=-∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k, where is real number. The first-degree-based entropy is generated for k=1, which has been well nurtured in last few years. As ∑j=1ndG(vj)k yields the well-known graph invariant first Zagreb index, the Id,k for k=2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of Id,2 in structure property modeling of molecules.