Filomat 2012 Volume 26, Issue 4, Pages: 733-738
https://doi.org/10.2298/FIL1204733D
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On atom-bond connectivity index
Das Kinkar Ch. (Department of Mathematics, Sungkyunkwan University, Suwon, Republic of Korea)
Gutman Ivan 
(Faculty of Science, Kragujevac)
Furtula Boris (Faculty of Science, Kragujevac)
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 = ∑ijE √(di+dj−2)/(didj).
Upper bounds and Nordhaus-Gaddum type results for ABC are established.
Keywords: Vertex-degree-based graph invariant, ABC index, Nordhaus-Gaddum type relations