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Hamilton-connectivity of 3-domination critical graphs with

✍ 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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Hamilton-connectivity of 3-Domination Cr
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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± ≀ 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

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## Abstract A graph __G__ is 3‐domination critical if its domination number Ξ³ is 3 and the addition of any edge decreases Ξ³ by 1. Let __G__ be a 3‐connected 3‐domination critical graph of order __n__. In this paper, we show that there is a path of length at least __n__βˆ’2 between any two distinct ve

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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