Topological characterisation of three classes of complex networks and their graphical representation and analysis
Wakeel Ahmed, Shahid Zaman, Sana Ashraf · Journal of Micromechanics and Molecular Physics · 2024
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 modelled using the chemical graph theory. The melting and boiling points of the molecules are modelled 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 tri-oxide lattice network and star of silicate network are list with edge partitions technique. We determine the first and second Zagreb index, the modified second Zagreb index, the symmetric division index, the harmonic index and the inverse sum index. We characterise detailed proofs of these indices for each triangular network. Furthermore, their graphical representation and comparison between the certain topological indices is presented in Sec. 6. These indices are highly accurate in the study of QSPRs and QSARs because they have strong correlation with the acentric factor and entropy.