On Vertex-Edge-Degree Topological Descriptors for Certain Crystal Networks

Abstract

Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences. The dynamical arrangement of vertices and their associated edges make them flexible (like liquid) to attain the shape of any physical structure or phenomenon easily. In the field of ICT they are used to reflect distributed component and communication among them. Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions. This area attracts the researchers due to its applications in theoretical and organic chemistry. It also inspires the mathematicians due to involvement of mathematical structures. Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences (vertex degrees). Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory. This paper reflects the work on topological indices such as -degree Zagreb index, the first -degree Zagreb index, the first -degree Zagreb index, the second -degree Zagreb index, -degree Randic index, the -degree Randic index, the -degree atom-bond connectivity index, the -degree geometric-arithmetic index, the -degree harmonic index and the -degree sum-connectivity index for crystal structural networks namely, bismuth tri-iodide and lead chloride. In this article we have determine the exact values of -degree and -degree based topological descriptors for crystal networks.