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.