Extremal values on the eccentric distance sum of trees

@article{Geng2013ExtremalVO,
  title={Extremal values on the eccentric distance sum of trees},
  author={Xianya Geng and Shuchao Li and Meng Zhang},
  journal={Discret. Appl. Math.},
  year={2013},
  volume={161},
  pages={2427-2439}
}
  • Xianya Geng, Shuchao Li, Meng Zhang
  • Published 30 June 2012
  • Mathematics, Computer Science
  • Discret. Appl. Math.
Let G=(V"G,E"G) be a simple connected graph. The eccentric distance sum of G is defined as @x^d(G)[email protected]?"v"@?"V"""[email protected]"G(v)D"G(v), where @e"G(v) is the eccentricity of the vertex v and D"G(v)[email protected]?"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… 
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The eccentric distance sum is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both
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References

SHOWING 1-10 OF 25 REFERENCES
On the extremal values of the eccentric distance sum of trees
Abstract Let G = ( V G , E G ) be a simple connected graph. The eccentric distance sum of G is defined as ξ d ( G ) = ∑ v ∈ V G e G ( v ) D G ( v ) , where e G ( v ) is the eccentricity of the vertex
Further results on the eccentric distance sum
The eccentric distance sum (EDS) is a novel graph invariant which can be used to predict biological and physical properties, and has a vast potential in structure activity/property relationships. For
On the eccentric distance sum of graphs
The eccentric distance sum is a novel topological index that offers a vast potential for structure activity/property relationships. For a graph G, it is defined as ξd(G)=∑v∈Ve(v)D(v), where e(v) is
On the eccentric distance sum of trees and unicyclic graphs
Abstract Let G be a simple connected graph with the vertex set V ( G ) . The eccentric distance sum of G is defined as ξ d ( G ) = ∑ v ∈ V ( G ) e ( v ) D G ( v ) , where e ( v ) is the eccentricity
A short and unified proof of Yu et al.ʼs two results on the eccentric distance sum
Abstract The eccentric distance sum (EDS) is a novel topological index that offers a vast potential for structure activity/property relationships. For a connected graph G, the eccentric distance sum
On the eccentric connectivity index of a graph
TLDR
An exact lower bound is obtained on @x^C(G) in terms of order, and this bound is sharp, and an asymptotically sharp upper bound is also derived.
The eccentric connectivity index of nanotubes and nanotori
TLDR
In this paper exact formulas for the eccentric connectivity index of TUC"4C"8(S) nanotube and TC"4 C"8 (S)nanotorus are given.
Eccentric connectivity index
The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is
Selected properties of the Schultz molecular topological index
  • I. Gutman
  • Mathematics, Computer Science
    J. Chem. Inf. Comput. Sci.
  • 1994
TLDR
The nontrivial part of MTI is the quantity S, and the new notation is preferred because the symbol S can be associated with the name of th discoverer of the "molecular topological index".
Extremal energies of trees with a given domination number
Abstract The energy of a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. Let T ( n , γ ) be the set of trees of order n and with domination number γ .
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1
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3
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