Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

We study an edge irregular reflexive k-labelling for the generalized friendship graphs, also known as flowers (a symmetric collection of cycles meeting at a common vertex), and determine the exact value of the reflexive edge strength for several subfamilies of the generalized friendship graphs.

There are many topological indices which have been discussed so far. But the most important topological indices among all these are topological degree-based indices. Topological indices in QSAR/QSPR study helped to check the biological activity and physical aspects of chemical compounds. In this paper, we computed the edge version of some prominent topological degree-based indices like Randić Index, Sum connectivity Index, Zagreb Indices, Atom bond connectivity ABC Index, Harmonic Index and Geometric-arithmetic GA Index of Boron triangular nanotubes.

Let G=(V,E) $G=(V,E)$ <!--mathContainer--> <!--Loading Mathjax--> be a finite, simple and undirected graph. The edge-magic total or vertex-magic total labeling of G $G$ <!--mathContainer--> <!--Loading Mathjax--> is a bijection f $f$ <!--mathContainer--> <!--Loading Mathjax--> from V(G)∪E(G) $V\left(G\right)\cup E\left(G\right)$ <!--mathContainer--> <!--Loading Mathjax--> onto the set of consecutive integers {1,2,…,|V(G)|+|E(G)|} $\{1,2,\dots ,\left|V\left(G\right)\right|+\left|E\left(G\right)\right|\}$ <!--mathContainer--> <!--Loading Mathjax--> , such that all the edge weights or vertex weights are equal to a constant, respectively. When all the edge weights or vertex weights are different then the labeling is called edge-antimagic or vertex-antimagic total, respectively. In this paper we provide some classes of graphs that are simultaneously super edge-magic total and super vertex-antimagic total, that is, graphs admitting labeling that has both properties at the same time. We show several results for fans, sun graphs, caterpillars and prisms.