Degree-Based Topological Invariants of Metal-Organic Networks

Abstract

Metal-organic networks (MONs) is a family of chemical compounds consisting of clusters or metal ions and organic ligands. These are studied as one, two or three dimensional structures of porous materials and subclasses of coordination polymers. MONs are mostly used in catalysis for the separation & purification of gases and as conducting solids or super-capacitors. In some situations, these networks are found to be stable in the process of removal or solvent of the guest molecules and could be restored with some other chemical compounds. The physical stability and mechanical properties of these networks have become a topic of great interest due to the aforesaid characteristics. Topological indices (TIs) are numeric quantities that are used to forecast the natural relationships among the physico-chemical characteristics of the chemical compounds in their fundamental network. During the studies of the MONs, TIs show an essential role in the theoretical & environmental chemistry and pharmacology. In this paper, we compute various latest developed degree-based TIs for two different metal-organic networks with increasing number of layers consisting on both metal and organic ligands vertices as well. A comparison among the computed different versions of the TIs with the help of the numerical values and their graphs is also included. INDEX TERMS Topological indices, chemical compounds, metals-organic networks.

Polynomials of Degree-Based Indices for Swapped Networks Modeled by Optical Transpose Interconnection System

“…Degree based topological indices involves degree of vertices of graph in the calculation. Randić index, Zagreb index, harmonic index, atom bond connectivity and geometric-arithmetic index are some known degree-based topological indices and polynomials [5]- [17].…”

Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

“…ere are several TIs in literature, but degree-based TIs are studied more than others (see [20][21][22][23][24][25][26][27][28][29]).…”

Computing FGZ Index of Sum Graphs under Strong Product

“…An atom is presented by a vertex and bonding between atom is showed by edge in the molecular graphs. e first and second Zagreb indices M 1 (G) and M 2 (G) of G are defined as follows [5,7,22]:…”

“…Sarala et al [16] computed the F-index of Φ-sum graphs under the operation of strong product. For further study, we refer to [17][18][19][20][21][22][23][24][25][26][27][28][29].…”