Abstract
Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the
HZ
−
index
of the four generalized sum graphs in the form of the various Zagreb indices of their factor graphs. These graphs are obtained by the strong product of the graphs
G
and
D
k
G
, where
D
k
∈
S
k
,
R
k
,
Q
k
,
T
k
represents the four generalized subdivision-related operations for the integral value of
k
≥
1
and
D
k
G
is a graph that is obtained by applying
D
k
on
G
. At the end, as an illustration, we compute the
HZ
−
index
of the generalized sum graphs for exactly
k
=
1
and compare the obtained results.