Mathematical Sciences: Faculty Publications
ABC Index of Trees with Fixed Number of Leaves
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
Copyright
This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.
