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ABC Index of Trees with Fixed Number of Leaves
MATCH Communications in Mathematical and in Computer Chemistry
  • Mikhail Goubko, Russian Academy of Sciences
  • Colton Magnant, Georgia Southern University
  • Pouria Salehi Nowbandegani, Georgia Southern University
  • Ivan Gutman, University of Kragujevac
Document Type
Article
Publication Date
1-1-2015
Disciplines
Abstract

Given a graph G, the atom-bond connectivity (ABC) index is defined to be ABC(G) = P uv∈E(G) qdG(u)+dG(v)−2 dG(u) dG(v) , where E(G) is the edge set of graph G and dG(v) is the degree of vertex v in graph G. The paper [10] claims to classify tho trees with a fixed number of leaves which minimize the ABC index. Unfortunately, there is a gap in the proof, leading to other examples that contradict the main result of that work. These examples and the problem are discussed in this note.

Citation Information
Mikhail Goubko, Colton Magnant, Pouria Salehi Nowbandegani and Ivan Gutman. "ABC Index of Trees with Fixed Number of Leaves" MATCH Communications in Mathematical and in Computer Chemistry Vol. 74 Iss. 3 (2015) p. 697 - 702
Available at: http://works.bepress.com/colton_magnant/50/