Total domination and least domination in a tree

Authors:
Xuezheng Lv;Jingzhong Mao
Affiliations:
Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Science, Beijing 100080, People's Republic of China;Department of Mathematics, Central China Normal University, Wuhan 430079, People's Republic of China
Venue:
Discrete Mathematics
Year:
2003

Citing 3
Cited 0

The least point covering and domination numbers of a graph

Discrete Mathematics - Topics on domination
Least domination in a graph

Discrete Mathematics - Special issue: selected papers in honour of Paul Erdo&huml;s on the occasion of his 80th birthday
Graph Theory With Applications

Graph Theory With Applications

Quantified Score

Hi-index	0.05

Visualization

Abstract

The total domination number γt of a graph G = (V,E) is the minimum cardinality of a dominating set D of G such that every vertex of V has at least one neighbor in D. The least domination number γL of G is the minimum cardinality of a dominating set X of G whose domination number is the minimum. In this paper, we prove the following conjecture due to Odile Favaron: Conjecture. For any tree T, we have γL(T)/γt(T) ≤ 3/2.