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 Trinajstic, which rely on the vertex degrees within a network, broaden 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 network’s structural dynamics, uncovering connectivity patterns that extend beyond direct neighbors. Also, a visual comparison of some topological indices for the VC5C7(h,c) nanosheet is provided.