The Eccentric-distance Sum of Some Graphs

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v), where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$