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 $ABC(G)=\sum _{uv \in E(G)} ({({d(u)+d(v)-2})/({d(u) d(v)})})^{1/2}$ , where $d(v)$ denotes the degree of a 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.