Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 421456, 9 pages
http://dx.doi.org/10.5402/2011/421456
Research Article

On the Maximal Eccentric Distance Sums of Graphs

1School of Mathematics, South China Normal University, Guangzhou 510631, China
2Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China

Received 12 March 2011; Accepted 14 April 2011

Academic Editor: H. Akçay

Copyright Β© 2011 Jianbin Zhang and Jianping Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

If 𝐺 is a simple connected graph with vertex 𝑉(𝐺), then the eccentric distance sum of 𝐺, denoted by πœ‰π‘‘(𝐺), is defined as βˆ‘π‘£βˆˆπ‘‰(𝐺)ec𝐺(𝑣)𝐷𝐺(𝑣), where ec𝐺(𝑣) is the eccentricity of the vertex 𝑣 and 𝐷𝐺(𝑣) is the sum of all distances from the vertex 𝑣. Let 𝑛β‰₯8. We determine the 𝑛-vertex trees with, respectively, the maximum, second-maximum, third-maximum, and fourth-maximum eccentric distance sums. We also characterize the extremal unicyclic graphs on 𝑛 vertices with respectively, the maximal, second maximal, and third maximal eccentric distance sums.