On the Bicyclic Graphs with Minimum Reduced Reciprocal Randic Index

The reduced reciprocal Randic (RRR) index is a molecular structure descriptor (or more precisely, a topological index), which is useful for predicting the standard enthalpy of formation and normal boiling point of isomeric octanes. In this paper, a mathematical aspect of RRR index is explored, or more specifically, the graph(s) having minimum RRR index is/are identified from the collection of all n–vertex connected bicyclic graphs for n≥5. As a consequence, the best possible lower bound on the RRR index, for n–vertex connected bicyclic graphs is obtained when n≥5.