On Randić indices of trees, unicyclic graphs, and bicyclic graphs

Abstract

AbstractThe Randić (connectivity) index is one of the most successful molecular descriptors in structure‐property and structure‐activity relationships studies. We determine the n‐vertex trees with the third for n ≥ 7, the fourth for n ≥ 10, the fifth and the sixth for n ≥ 11 maximum Randić indices, unicyclic graphs with the third for n ≥ 5, the fourth for n ≥ 7, and the fifth for n ≥ 8 maximum Randić indices, and bicyclic graphs with the second and the third for n ≥ 7, the fourth and the fifth for n ≥ 9 maximum Randić indices. We also determine the n‐vertex tree(s) for n ≥ 6 with the fifth minimum Randić index, unicyclic graphs for n ≥ 5 with the second, the third and the fourth minimum Randić indices, and bicyclic graph(s) for n ≥ 5 with the second minimum Randić index. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011