Abstract:The atom-bond connectivity (ABC ) index of a graph G = (V, E) is defined as ABC(G), where d i denotes the degree of vertex v i of G. Due to its interesting applications in chemistry, this molecular structure descriptor has become one of the most actively studied vertex-degree-based graph invariants. Many efforts were made towards the elementary problem of characterizing tree(s) with minimal ABC index, which remains open and was coined as the "ABC index conundrum". Up to date, quite a few significant results ha… Show more
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