The zeroth-order general Randić index (usually denoted by Rα0) and variable sum exdeg index (denoted by SEIa) of a graph G
Nearby in the stack
are defined as
Rα0(G)=∑v∈V(G)(dv)α
and
SEIa(G)=∑v∈V(G)dvadv
where
dv
is degree of the vertex
v∈V(G)
,
a
is a positive real number different from 1 and
α
is a real number other than
0
and
1
. A segment of a tree is a path
P
, whose terminal vertices are branching or pendent, and all non-terminal vertices (if exist) of
P
have degree 2. For
n≥6
, let
PTn,n1
,
STn,k
,
BTn,b
be the collections of all
n
-vertex trees having
n1
pendent vertices,
k
segments,
b
branching vertices, respectively. In this paper, all the trees with extremum (maximum and minimum) zeroth-order general Randić index and variable sum exdeg index are determined from the collections
PTn,n1
,
STn,k
,
BTn,b
. The obtained extremal trees for the collection
STn,k
are also extremal trees for the collection of all
n
-vertex trees having fixed number of vertices with degree 2 (because it is already known that the number of segments of a tree