A Leap Into Graph Theory: Leap Zagreb Coindices of Monogenic Semigroup Graphs

Let denote the zero‐divisor graph associated with a monogenic semigroup. In the present study, certain topological indices of that have not previously been examined in this context are investigated. More precisely, explicit closed‐form expressions are derived for the leap Zagreb coindices , , and of , which were recently introduced as distance‐based degree descriptors. In contrast to the classical Zagreb coindices, which depend solely on the first‐degree of vertices, the leap Zagreb coindices are based on the notion of the 2-degree of a vertex. By exploiting the well‐known structural properties of , precise formulas for each of these coindices are established, and supporting results are presented. The findings contribute to the growing literature on the application of novel topological indices to algebraically defined graph families.