On the Sombor Index of Sierpiński and Mycielskian Graphs

Document Type : Original paper

Authors

Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India

Abstract

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 Sierpi'nski graphs; originally defined by Klav\v{z}ar and Milutinovi'c 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 \(K_n\), \(C_n^2\), \(C_n\), and \(P_n\). We also provide Python codes to verify the results for the \(SO\left(S\left(n,K_m\right)\right)\) and \(SO\left(\mu_m\left(K_n\right)\right)\).

Keywords

Main Subjects

References

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Communications in Combinatorics and Optimization
Volume 10, Issue 1
March 2025
Pages 20-56

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