on the sombor index of sierpiński and mycielskian graphs

In 2020, mathematical chemist, ivan gutman, introduced a new vertex degree-based topological index called the sombor index, denoted by so (g), where g is a simple, connected, finite, graph. this paper aims to present some novel formulas, along with some upper and lower bounds on the sombor index of generalized sierpiński graphs; originally defined by klavžar and milutinović by replacing the complete graph appearing in s (n, k) with any graph and exactly replicating the same graph, yielding self-similar graphs of fractal nature; and on the sombor index of the m-mycielskian or the generalized mycielski graph; formed from an interesting construction given by jan mycielski (1955); of some simple graphs such as kn, c2n, cn, and pn. we also provide python codes to verify the results for the so (s (n, km)) and so (µm (kn)).