Independence and connectivity in 3-domination-critical graphs

  • Authors:

  • Lian-zhu Zhang;Feng Tian

  • Affiliations:

  • Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, China;Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

Let δ, γ, κ and α be, respectively, the minimum degree, the domination number, the con nectivity and the independence number of a graph G. The graph G is 3-domination-critical if γ = 3 and the addition of any edge decreases γ by 1. In this paper, we prove that if G is a 3-domination-critical graph, then α ≤ κ + 2; and moreover, if κ ≤ δ -1, then α ≤ κ + 1. We also give a short proof of Wojcicka's result, which says that every connected 3-domination-critical graph of order at least 7 contains a hamiltonian path (J. Graph Theory 14 (1990) 205).