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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Roman, Italian, and 2-Domination

William F. Klostermeyer 1, Gary MacGillivray2
1School of Computing University of North Florida Jacksonville, FL 32224-2669
2Department of Mathematics and Statistics University of Victoria, P.O. Box 3060 STN CSC Victoria, BC, Canada V8W 3R4
  • Published: 30/03/2019

Abstract

Motivated by finding a way to connect the Roman domination number and 2-domination number, which are in general not comparable, we consider a parameter called the Italian domination number (also known as the Roman \((2)\)-domination number). This parameter is bounded above by each of the other two. Bounds on the Italian domination number in terms of the order of the graph are shown. The value of the Italian domination number is studied for several classes of graphs. We also compare the Italian domination number with the 2-domination number.

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Citation
William F. Klostermeyer , Gary MacGillivray. Roman, Italian, and 2-Domination[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 108. -. DOI: .