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Which Tree Has the Smallest ABC Index among Trees with K Leaves?
Discrete Applied Mathematics
  • Colton Magnant, Georgia Southern University
  • Pouria Salehi Nowbandegani, Georgia Southern University
  • Ivan Gutman, University of Kragujevac
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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.

Citation Information
Colton 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 ISSN: 0166-218X
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