VI. reciprocal status index and co-index of graphs

Abstract

For the vertex set V (G) of a graph G, the sum of reciprocals of the breadth (distances) between the vertex v is an element of V (G) and whole other remaining vertices of G is called reciprocal status of v. In this study, first of all, we introduced the VL reciprocal status index and VL reciprocal status co-index of a graph G. Later, we exposed some sharp bounds for these indices. Furthermore, we determined the VL reciprocal status (co-)index over some standard graphs. Finally, we presented correlations between VL reciprocal status index and some properties of Butane derivatives via a table and illustrated with a figure.