Abstract
For a graph
G
, its general sum-connectivity is usually denoted by
χ
α
G
and is defined as the sum of the numbers
d
G
u
+
d
G
v
α
over all edges
u
v
of
G
, where
d
G
u
,
d
G
v
represent degrees of the vertices
u
,
v
, respectively, and
α
is a real number. This paper addresses the problem of finding graphs possessing the minimum
χ
α
value over the class of all trees with a fixed order
n
and fixed number of pendent vertices
n
1
for
α
>
1
. This problem is solved here for the case when
4
≤
n
1
≤
n
+
5
/
3
and
α
>
1
, by deriving a lower bound on
χ
α
for trees in terms of their orders and number of pendent vertices.