^{}Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I R. Iran

Receive Date: 04 December 2011,
Revise Date: 21 February 2012,
Accept Date: 11 May 2012

Abstract

The eccentric distance sum is a graph invariant defined as $\sum_{uv\in E} ε_{G}(v)D_{G}(v)$, where ε_{G}(v) is the eccentricity of a vertex v in G and D_{G}(v ) is the sum of distances of all vertices in G from v. In this paper, we compute the eccentric distance sum of Volkmann tree and then we obtain some results for vertex−transitive graphs

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