Which Tree Has the Smallest ABC Index among Trees with K Leaves?

Authors

Colton Magnant, Georgia Southern UniversityFollow
Pouria Salehi Nowbandegani, Georgia Southern UniversityFollow
Ivan Gutman, University of KragujevacFollow

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