On the adjacent eccentric distance sum of graphs

In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph $G$ is defined as$${\xi }^{sv}(G)=\sum _{v\in V(G)}\frac{\epsilon (v)D(v)}{deg(v)},$$where $\epsilon (v)$ is the eccentricity of the vertex $v$, $deg(v)$ is the degree of the vertex $v$ and$$D(v)=\sum _{u\in V(G)}d(u,v)$$is the sum of all distances from the vertex $v$.