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 graphG, it is defined asABC(G)=∑ uv ∈ E(G) ((d(u)+d(v)-2)/(d(u) d(v)))1/2, where$d(v)$denotes the degree of a vertexvofG. Recently in[17]graphs withnvertices,$2n-4$and$2n-3$edges, and maximum$ABC$index were characterized. Here, we consider the next, more complex case, and characterize the graphs withnvertices,$2n-2$edges, and maximum$ABC$index.