Topological indices of k-th subdivision and semi total point graphs

Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and $H$. In this article, we present exact expressions for some topological indices of k-th subdivision graph and semi total point graphs respectively, which are a generalization of ordinary subdivision and semi total graph for $k\ge 1$.Comment: 14 page

F-index of graphs based on new operations related to the join of graphs

The forgotten topological index or F-index of a graph is defined as the sum of degree cube of all the vertices of the graph. This index was introduced by Gutman and Trinajesti\'{c} more than 40 years ago. In this paper, we derive F-index of new operations of subdivision graphs related to the graphs join.Comment: 17 Pages, 4 figure

The (a,b)-Zagreb index of some derived networks

There is a very wide application of mathematics in communication theory, signal processing and networking. A network is formed by nodes communicating with each other. Graph theory plays a vital role in the area of networking research. A topological index is a numeric quantity obtained from a graph structure which is invariant under graph isomorphism. In this study, we obtained a generalized degree-based topological index, called -Zagreb index of some derived networks such as Sierpinski network, butterfly network, Benes network and mesh-derived network and hence consider some particular cases.Council of Scientific & Industrial Research (CSIR) - India 09/973(0016)/2017-EMR-