Dendrimers are constructed by the successive addition of layers of branching groups. Topological indices are numerical numbers associated which are graph invariant up to isomorphism. In this report, we give closed form of M-polynomial of PETAA dendrimers and from this M-polynomial, we recover many topological indices. These topological indices help to predict physcio-chemical properties of the underling dendrimers, and help to the study of the properties of the materials of ship building. We also give graphical representation of our results.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index are defined by using these new graph invariants as parallel to their corresponding classical degree versions. These new group ev-degree and ve-degree indices are compared with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. The ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. The relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices are investigated.

Networks plays an important role in the field of engineering and topological indices can help us to get interesting properties if of underlined networks. With the help of topological indices, one can understand the topology and differentiate properties of different networks. The aim of this paper is to study the Generalized prism network which is very important for the researchers working in physics and engineering. We computed several degree-based indices, for example, sum connectivity index, Arithmetic-Geometric index, modified Randić, SK index, SK₁ index, and SK_{2 .}

Mathematical topological characterization of chemical graphs gives information about some physical properties of molecules. Classical degree based topological indices of copper oxide have been recently calculated. Ve-degree and Ev-degree based topological indices have been newly defined in graph theory. In this study we investigate ve-degree topological properties of copper oxide. We calculate ve-degree Zagreb and Randić indices of copper oxide.

Topological indices are important tools to modeling chemical properties of molecules. ve-degree based atom-bond connectivity, sum-connectivity, geometric-arithmetic, and harmonic indices are defined as their corresponding classical degree based counterparts recently in chemical graph theory. In this study we investigate ve-degree atom-bond connectivity, sum-connectivity, geometric-arithmetic, and harmonic topological properties of copper oxide.We calculate exact values of these novel topological indices for copper oxide and give closed formulas.