Mathematical simulation of three classes of complex networks and their topological analysis

Mathematical chemistry is concerned with the use of mathematics to solve problems in chemistry. In chemistry, the molecules are frequently shown as graphs with vertices denoting atoms and edges denoting bonds, respectively. Atom valences and bond multiplicities are represented by vertex degrees and edge multiplicities, respectively. The vertices in a graph are said to be close by if an edge connects them. Alkanes are a class of compounds whose physical characteristics are modeled using the chemical graph theory. The melting and boiling points of the molecules are modeled using topological indices based on the graphical structure of the alkanes. A mesh network is a local area network in which the infrastructure nodes (i.e., bridges, switches, and other infrastructure devices) connect directly, dynamically, and non-hierarchically to as many other nodes as possible and cooperate with one another to efficiently route data. In this paper, the distinct degrees of triangular mesh network, enhanced mesh network, rhenium trioxide lattice network, and star of silicate network are listed with the edge partitions technique. We determined the first (second) Zagreb indices, the modified second Zagreb index, the symmetric division index, the harmonic index, and the inverse sum index. In Sec. 2 , we characterized the detailed proofs of these indices for each triangular network. Based on our obtained results, we give a graphical representation and comparison between certain topological indices. These computed indices are highly accurate in the study of QSPRs and QSARs because they have the best correlation with the acentric factor and entropy.