ABC Index of Trees with Fixed Number of Leaves

Authors

Mikhail Goubko, Russian Academy of Sciences
Colton Magnant, Georgia Southern UniversityFollow
Pouria Salehi Nowbandegani, Georgia Southern UniversityFollow
Ivan Gutman, University of KragujevacFollow

Document Type

Article

Publication Date

2015

Publication Title

MATCH Communications in Mathematical and in Computer Chemistry

ISSN

0340-6253

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.

Recommended Citation

Goubko, Mikhail, Colton Magnant, Pouria Salehi Nowbandegani, Ivan Gutman. 2015. "ABC Index of Trees with Fixed Number of Leaves." MATCH Communications in Mathematical and in Computer Chemistry, 74 (3): 697-702. source: http://match.pmf.kg.ac.rs/electronic_versions/Match74/n3/match74n3_697-702.pdf
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/373