Extremal graphs for inequalities involving domination parameters
Discrete Mathematics
The eccentric connectivity index of nanotubes and nanotori
Journal of Computational and Applied Mathematics
Further results on the eccentric distance sum
Discrete Applied Mathematics
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Let G=(V"G,E"G) be a simple connected graph. The eccentric distance sum of G is defined as @x^d(G)=@?"v"@?"V"""G@e"G(v)D"G(v), where @e"G(v) is the eccentricity of the vertex v and D"G(v)=@?"u"@?"V"""Gd"G(u,v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number @c having the minimal eccentric distance sum is determined and the tree among n-vertex trees with domination number @c satisfying n=k@c having the maximal eccentric distance sum is identified, respectively, for k=2,3,n3,n2. 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.