A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index
M
r
G
, geometric arithmetic index
GA
G
, harmonic index
H
G
, general version of harmonic index
H
r
G
, sum connectivity index
λ
G
, general sum connectivity index
λ
r
G
, forgotten topological index
F
G
, and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the
AG
2
G
and Sanskruti index for the Robertson apex graph G.