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 d(G) (v(i)) is degree of the vertex v(i) for each i = 1, 2,..., n. Now, the k-th degree-based graph entropy for G is defined as I-d,I- k (G) = Sigma(n)(i=1) (d(G)(v(i))(k) / Sigma(n)(j=1) d(G)(v(j))(k) log d(G)(v(i))(k) / Sigma(n)(j=1) d(G) (v(j))(k)), where k is real number. The first-degree-based entropy is generated for k = 1, which has been well nurtured in last few years. As Sigma(n)(j=1) d(G) (v(j))(k) yields the well-known graph invariant first Zagreb index, the I-d,I- 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 I-d,I- 2 in structure property modeling of molecules.