On the Maximal Eccentric Distance Sums of Graphs

Jianbin Zhang ； Jianping Li

《ISRN Applied Mathematics》 2011 (2011/12) Pp. 938-946

並列摘要

If G is a simple connected graph with vertex V (G), then the eccentric distance sum of G, denoted by ξd(G), is defined as ∑(subscript v∈V(G)) (superscript ec)G(v)DG(v), where ec(subscript G)(v) is the eccentricity of the vertex v and DG(v) is the sum of all distances from the vertex v. Let n ≥ 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.