Hamilton-connectivity of 3-domination critical graphs with
β Scribed by Yaojun Chen; T.C. Edwin Cheng; C.T. Ng
- Book ID
- 108113806
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 236 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
A graph G is 3-domination critical if its domination number Ξ³ is 3 and the addition of any edge decreases Ξ³ by 1. It was proved by Favaron et al. that Ξ± β€ Ξ΄ + 2 for any connected 3-domination critical graph. Denote by Ο (G) the toughness of a graph G. Recently Chen et al. conjectured that a connecte
## Abstract A graph __G__ is 3βdomination critical if its domination number Ξ³ is 3 and the addition of any edge decreases Ξ³ by 1. Let __G__ be a 3βconnected 3βdomination critical graph of order __n__. In this paper, we show that there is a path of length at least __n__β2 between any two distinct ve
Let Ξ΄, Ξ³, i and Ξ± be respectively the minimum degree, the domination number, the independent domination number and the independence number of a graph G. The graph G is 3-Ξ³-critical if Ξ³ = 3 and the addition of any edge decreases Ξ³ by 1. It was conjectured that any connected 3-Ξ³-critical graph satisf