Abstract
Exploring into the area of advanced topological measures, the study significantly contributes to the exploration of complex networks, potentially enhancing ability to characterize their complexities with greater distinction and depth. In a manner akin to the topological indices developed by Gutman and Trinajstić, which rely on the vertex degrees within a network, we can broaden our understanding by introducing generalized topological indices. By considering the degrees of vertices not just at immediate proximity but also at a distance of two edges, these indices offer a richer perspective on the networks structural dynamics, uncovering connectivity patterns that extend beyond direct neighbors.
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