2012/06/30 by Shuchao Li, Meng Zhang, Li, Shuchao +1
Chemistry · Materials Science · Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C50 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1207.0083
15 Pages, 8 figures
arxiv created 2012/06/30 · openalex publication_date 2012/06/30 · arxiv updated 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(VG, EG) be a simple connected graph. The eccentric distance sum of G is defined as ξd(G) = ∑v∈ VGεG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v) = ∑u∈ VGdG(u,v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-vertex trees with domination number γ satisfying n = kγ having the maximal eccentric distance sum is identified, respectively, for k=2,3,(n)/(3),(n)/(2). Sharp upper and lower bounds on the eccentric distance sums among the n-vertex trees with k leaves are determined. Finally, the trees among the n-vertex trees with a given bipartition having the minimal, second minimal and third minimal eccentric distance sums are determined, respectively.