It is exciting to study and establish relationships between the physical properties and the molecular structure of chemicals and there is a scope for defining new topological indices. This paper aims to introduce a new topological index for graphs called Chelo index. The Chelo index of a graph G is the sum of five times order of G and two times the number of geodesics of length 3 minus the number of geodesics between peripheral vertices. We compute Chelo index for some standard graphs and observe the correlation between some physical properties and Chelo index for low alkanes. Also, we establish a formulae for computing the number of 176 graph geodesics in a graph and the Chelo index using the adjacency matrix

In this short paper, we establish formulae to compute Wiener index, reciprocal Wiener index and peripheral Wiener index of graphs using adjacency matrix. Further, we present algorithms for the same

The stress of a vertex in a graph is the number of geodesics passing through it. The status of a vertex v in a graph is the sum of the distances from v to all other vertices. We define the richness of a vertex v in a graph as the status of v minus the stress of v. The total richness of a graph is the sum of richness of all the vertices in that graph. We made some observations, compute richness of vertices in some standard graphs and obtain some interesting results.