Abstract
Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs.
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