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)).