Which Tree Has the Smallest ABC Index among Trees with K Leaves?Discrete Applied Mathematics
AbstractGiven a graph G, the atom–bond connectivity (ABC) index is defined to be 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 ifk≤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.
Citation InformationColton Magnant, Pouria Salehi Nowbandegani and Ivan Gutman. "Which Tree Has the Smallest ABC Index among Trees with K Leaves?" Discrete Applied Mathematics Vol. 194 (2015) p. 143 - 146
Available at: http://works.bepress.com/colton_magnant/54/