The Second Hyper-Zagreb Coindex of Chemical Graphs and Some Applications

The second hyper-Zagreb coindex is an efficient topological index that enables us to describe a molecule from its molecular graph. In this current study, we shall evaluate the second hyper-Zagreb coindex of some chemical graphs. In this study, we compute the value of the second hyper-Zagreb coindex of some chemical graph structures such as sildenafil, aspirin, and nicotine. We also present explicit formulas of the second hyper-Zagreb coindex of any graph that results from some interesting graphical operations such as tensor product, Cartesian product, composition, and strong product, and apply them on a q-multiwalled nanotorus.

Comparative Study of Valency-Based Topological Indices for Tetrahedral Sheets of Clay Minerals

: Intercapillary research in mathematics and other pure sciences areas has always helped humanity quantify natural phenomena. This article also contributes to which valency-based topological indices are implemented on tetrahedral sheets of clay minerals. These indices have been used for a long time and are considered the most powerful tools to quantify chemical graphs. The atoms in the chemical compound and the bonds between the atoms are depicted as the graph’s vertices and edges, respectively. The valency (or degree) of a vertex in a graph is the number of edges incident to that vertex. In this article, various degree-based indices and their modifications are determined to check each types’ significance.

Computation of Nirmala Indices of Some Chemical Networks

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

Extremal Values of Randić Index among Some Classes of Graphs

Suppose G is a simple graph with edge set E G . The Randić index R G is defined as R G = ∑ u v ∈ E G 1 / deg G u deg G v , where deg G u and deg G v denote the vertex degrees of u and v in G , respectively. In this paper, the first and second maximum of Randić index among all n − vertex c − cyclic graphs was computed. As a consequence, it is proved that the Randić index attains its maximum and second maximum on two classes of chemical graphs. Finally, we will present new lower and upper bounds for the Randić index of connected chemical graphs.