Abstract
The modified first Zagreb connection index
ZC
1
∗
is a graph invariant that appeared about fifty years ago within a study of molecular modeling, and after a long time, it has been revisited in two papers ((Ali and Trinajstić, 2018) and (Naji et al., 2017)) independently. For a graph
G
, this graph invariant is defined as
ZC
1
∗
G
=
∑
v
∈
V
G
d
v
τ
v
, where
d
v
is the degree of the vertex
v
and
τ
v
is the connection number of
v
(that is, the number of vertices having distance 2 from
v
). In this paper, the graphs with maximum/minimum
ZC
1
∗
value are characterized from the class of all
n
-vertex trees with fixed number of pendent vertices (that are the vertices of degree 1).