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On the Maximal Eccentric Distance Sums of Graphs

2011
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ISRN Applied Mathematics
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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 ∑v∈V(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 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

doi:10.5402/2011/421456
fatcat:seyd2f4v35axne5desmud6znv4