Vertex-Addition Strategy for Domination-Like Invariants

  • Michitaka Furuya
  • Naoki Matsumoto
Keywords: Domination, Total domination, Roman domination


In [J. Graph Theory 13 (1989) 749—762], McCuaig and Shepherd gave an upper bound of the domination number for connected graphs with minimum degree at least two. In this paper, we propose a simple strategy which, together with the McCuaig-Shepherd theorem, gives a sharp upper bound of the domination number via the number of leaves. We also apply the same strategy to other domination-like invariants, and find a relationship between such invariants and the number of leaves.

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