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Further results on atom-bond connectivity index of trees. (English) Zbl 1216.05161

Summary: The atom-bond connectivity (ABC) index of a graph G is defined as

ABC(G)= uvE(G) d u +d v -2 d u d v ,

where E(G) is the edge set and d u is the degree of vertex u of G. We give the best upper bound for the ABC index of trees with a perfect matching, and characterize the unique extremal tree, which is a molecular tree. We also give upper bounds for the ABC index of trees with fixed number of vertices and maximum degree, and of molecular trees with fixed numbers of vertices and pendent vertices, and characterize the extremal trees.

MSC:
05C90Applications of graph theory
05C05Trees
References:
[1]Cvetković, D.; Gutman, I.; Trinajstić, N.: Kekulé structures and topology, Chem. phys. Lett. 16, 614-616 (1972)
[2]Estrada, E.; Torres, L.; Rodríguez, L.; Gutman, I.: An atom-Bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem. 37A, 849-855 (1998)
[3]Estrada, E.: Atom-Bond connectivity and the energetic of branched alkanes, Chem. phys. Lett. 463, 422-425 (2008)
[4]Furtula, B.; Graovac, A.; Vukičević, D.: Atom-Bond connectivity index of trees, Discrete appl. Math. 157, 2828-2835 (2009) · Zbl 1209.05252 · doi:10.1016/j.dam.2009.03.004
[5]Hansen, P.; Mélot, H.: Variable neighborhood search for extremal graphs. 6. Analyzing bounds for the connectivity index, J. chem. Inf. comput. Sci. 43, 1-14 (2003)
[6]B. Zhou, R. Xing, On atom-bond connectivity index, preprint.