Hamilton - connectivity of 3 - Domination Critical Graphs with α = δ + 2
نویسندگان
چکیده
A graph G is 3-domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. It was proved by Favaron et al. that α ≤ δ + 2 for any connected 3-domination critical graph. Denote by τ (G) the toughness of a graph G . Recently Chen et al. conjectured that a connected 3-domination critical graph G is Hamilton-connected if and only if τ (G) > 1 and showed the conjecture is true when α ≤ δ. In this paper, by using a closure operation define by Bondy and Chvátal, we show the conjecture is true when α = δ + 2.
منابع مشابه
Hamilton-Connectivity of 3-Domination Critical Graphs
A graph G is 3-domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3-domination critical graph with toughness more than one. It was proved G is Hamiltonconnected for the cases α ≤ δ (Discrete Mathematics 271 (2003) 1-12) and α = δ + 2 (European Journal of Combinatorics 23(2002) 777-784). In this paper, we show G is Hamilton-connected for...
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