On atom-bond connectivity index

The atom-bond connectivity index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ∑ ij2E √ (di + dj 2)/(di dj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.

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