  In this paper, we investigate the topological photon sphere from two distinct
perspectives. In the first view, we examine the existence and characteristics
of topological photon(anti-photon)spheres for black holes with different
structures, such as Einstein-Young-Mills non-minimal, AdS black holes
surrounded by Chaplygin-like dark fluid, and Bardeen-like black holes in
Einstein-Gauss-Bonnet gravity. Furthermore, we delve into the deeper
perspective of the necessity of photon spheres for super-compact gravitational
structures such as black holes. By leveraging this necessity, we propose a
classification of the parameter space of black hole models based on the
existence and positioning of photon spheres. This approach enables the
determination of parameter ranges that delineate whether a solution represents
a black hole or a naked singularity. In essence, the paper illustrates the
utility of the photon sphere as a notable test for establishing the permissible
and non-permissible parameter ranges within specific theories of black hole
solutions.
