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Filomat 2012 Volume 26, Issue 4, Pages: 683-688
https://doi.org/10.2298/FIL1204683X
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Extremal trees with fixed degree sequence for atom-bond connectivity index

Xing Rundan (Department of Mathematics, South China Normal University, Guangzhou, China)
Zhou Bo (Department of Mathematics, South China Normal University, Guangzhou, China)

The atom-bond connectivity (ABC) index of a graph G is the sum of √d(u)+d(v)−2/d(u)d(v) over all edges uv of G, where d(u) is the degree of vertex u in G. We characterize the extremal trees with fixed degree sequence that maximize and minimize the ABC index, respectively. We also provide algorithms to construct such trees.

Keywords: atom-bond connectivity index, tree, degree sequence