#### Title

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