Eccentric connectivity index and connective eccentric index of graphs

Abstract

In the present work we study the eccentric connectivity index and connective eccentric index using $D$-distance. Among others, we obtain some results like average $D$-distance is less than $D$-eccentric connectivity index, if $G$ is a $ {k}$ - regular graph then $\xi^{D C}(G)=n k \operatorname{avec}^{D}(G)$ and some more results on $D$-self centered graphs, the relation between two indices. We compute these indices of some classes of graphs. We also compute the average D-eccentricities in some classes.