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On the bicyclic graphs with minimum reduced reciprocal randic index. (English) Zbl 1407.92154

Summary: The reduced reciprocal Randić (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 \(n\geq 5\). As a consequence, the best possible lower bound on the RRR index, for \(n\)-vertex connected bicyclic graphs is obtained when \(n\geq 5\).

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C90 Applications of graph theory
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