On autographix conjecture regarding domination number and average eccentricity-Reference-Cited by-同舟云学术

On autographix conjecture regarding domination number and average eccentricity

Published:2019 Issue:3 Volume:33 Page:699-710
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Pei Li-Dan¹,Pan Xiang-Feng²,Tian Jing²,Peng Gui-Qin²

Affiliation:

1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, P.R. China + School of Mathematics and Statistics, Hefei Normal University, Hefei, Anhui, P.R. China

2. School of Mathematical Sciences, Anhui University, Hefei, Anhui, P.R. China

Abstract

The eccentricity of a vertex is the maximal distance from it to another vertex and the average eccentricity ecc(G) of a graph G is the mean value of eccentricities of all vertices of G. A set S ? V(G) is a dominating set of a graph G if NG(v) ? S ? 0 for any vertex v ? V(G)\S. The domination number (G) of G is the minimum cardinality of all dominating sets of G. In this paper, we correct an AutoGraphiX conjecture regarding the domination number and average eccentricity, and present a proof of the revised conjecture. In addition, we establish an upper bound on ?(T)-ecc(T) for an n-vertex tree T.

Publisher

National Library of Serbia

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. About AutoGraphiX Conjecture on Domination Number and Remoteness of Graphs;Mathematics;2022-10-10

2. On the average Steiner 3-eccentricity of trees;Discrete Applied Mathematics;2021-12

3. Proofs of the AutoGraphiX conjectures on the domination number, average eccentricity and proximity;Discrete Applied Mathematics;2021-01