Entropy of Weighted Graphs with the Degree-Based Topological Indices as Weights

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Among the large number of existing topological indices, an important class of such measures relies on Shannon's entropy to characterize graphs by determining their structural information content. In this' paper, we study the entropy of weighted graphs with the degree-based topological indices (specially, the first and second Zagreb indices, the general Randic index, the harmonic and sum-connectivity index) as weights.