Mathematical Sciences: Faculty Publications
Which Tree Has the Smallest ABC Index among Trees with K Leaves?
Document Type
Article
Publication Date
10-30-2015
Publication Title
Discrete Applied Mathematics
DOI
10.1016/j.dam.2015.05.008
ISSN
0166-218X
Abstract
Given a graph G, the atom–bond connectivity (ABC) index is defined to be ABC (G) = ∑u~v √ d(u)+d(v)-2/d(u)d(v) where u and v are vertices of G, d(u) denotes the degree of the vertex u, and u∼v indicates that u and v are adjacent. Although it is known that among trees of a given order n, the star has maximum ABC index, we show that if k≤18, then the star of order k+1 has minimum ABC index among trees with k leaves. If k≥19, then the balanced double star of order k+2 has the smallest ABC index.
Recommended Citation
Magnant, Colton, Pouria Salehi Nowbandegani, Ivan Gutman.
2015.
"Which Tree Has the Smallest ABC Index among Trees with K Leaves?."
Discrete Applied Mathematics, 194: 143-146.
doi: 10.1016/j.dam.2015.05.008
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/374
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.
