# 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} }

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…

## 41 Citations

On the extremal values of the eccentric distance sum of trees

- Computer Science, MathematicsDiscret. Appl. Math.
- 2015

In this paper, the trees having the maximal EDS among n -vertex trees with maximum degree Δ and among those with domination number 3 are characterized.

On the extreme eccentric distance sum of graphs with some given parameters

- Computer Science, MathematicsDiscret. Appl. Math.
- 2016

The relationship between the EDS and some other graph parameters such as the order, the size, the diameter and the connectivity are studied and a sharp lower bound on the E DS of n -vertex connected triangle-free graphs is determined.

On the extremal values of the eccentric distance sum of trees with a given domination number

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2017

The extremal tree among n -vertex trees with domination number γ satisfying 4 ≤ γ ⌈ n 3 ⌉ having the maximal EDS is characterized and proves Conjecture 4.2 of Miao et al. (2015).

On the extremal values of the eccentric distance sum of trees with a given maximum degree

- Computer Science, MathematicsDiscret. Appl. Math.
- 2020

The extremal tree which minimizes the EDS among n -vertex trees of given maximum degree is characterized and proves Conjecture 3.2 posed in Miao et al., (2015).

Some further results on the eccentric distance sum

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

Abstract Let G = ( V ( G ) , E ( G ) ) be a simple connected graph. Then the eccentric distance sum of G, which is a novel graph invariant by offering a great potential for structure…

Extremal graphs of given parameters with respect to the eccentricity distance sum and the eccentric connectivity index

- Computer Science, MathematicsDiscret. Appl. Math.
- 2019

In this paper, some extremal problems on the EDS and the ECI of graphs with given parameters are considered and sharp upper and lower bounds on the difference between E DS and ECI among all n -vertex graphs of diameter 2 with given minimum degree are determined.

On the quotients between the eccentric connectivity index and the eccentric distance sum of graphs with diameter 2

- Computer Science, MathematicsDiscret. Appl. Math.
- 2020

Sharp upper and lower bounds on ξ c ( G) ξ d ( G ) for graph in G n 2 are determined, and the corresponding extremal graphs are characterized as well.

Extremal bipartite graphs and unicyclic graphs with respect to the eccentric resistance-distance sum

- Mathematics
- 2021

Abstract Let G be a connected graph with vertex set V G . The eccentric resistance-distance sum of G is defined as ξ R ( G ) = ∑ { u , v } ⊆ V G ( e G ( u ) + e G ( v ) ) R u v , where e G ( ⋅ ) is…

On the extremal graphs with respect to the total reciprocal edge-eccentricity

- Computer Science, MathematicsJ. Comb. Optim.
- 2020

This paper first characterize the unique graph with the maximum total reciprocal edge-eccentricity among all graphs with a given number of cut vertices, and determines the k -connected bipartite graphs of order n with diameter d having themaximum total reciprocal edges.

On the minimum eccentric distance sum of bipartite graphs with some given parameters

- Mathematics
- 2015

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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