On the Maximum ABC Index of Graphs With Prescribed Size and Without Pendent Vertices

The atom-bond connectivity (ABC) index is one of the most actively studied degree-based graph invariants, which are found in a vast variety of chemical applications. For a simple graph G, it is defined as ABC(G) = Σuv∈E(G)((d(u) + d(v) – 2)/(d(u)d(v)))1/2, where d(v) denotes the degree ofa vertex v of G. Recently in [17] graphs with n vertices, 2n – 4 and 2n – 3 edges, and maximum ABC index were characterized. Here, we consider the next, more complex case, and characterize the graphs with n vertices, 2n – 2 edges, and maximum ABC index.

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