Abstract
The Sombor index (\( SO \)) and its extended version \( p \)-Sombor index (\( SO_p \)) are vertex degree-based topological indices that have potential applications in mathematical chemistry. In this article, we obtain several new relations for these indices. Precisely, we find relations between \( SO \) and \( SO_p \) and characterize the graphs where equality occurs. Also, we present relations for \( SO \) and \( SO_p \) involving other topological indices, such as the first Zagreb, Randić, reciprocal Randić, inverse sum indeg, and Albertson indices. Furthermore, we set up relations between the \( p \)-Sombor indices for different values of \( p \).
