On domination numbers of graph bundles

  • Blaz Zmazek
  • Janez Zerovnik


Letγ(G) be the domination number of a graphG. It is shown that for anyκ ≥ 0 there exists a Cartesian graph bundleB█φF such thatγ(B█φF) =γ(B)γ(F) — 2κ. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing’s conjecture on strong graph bundles is shown not to be true by proving the inequalityγ(B █ φF)γ(B)γ(F) for strong graph bundles. Examples of graphsB andF withγ(B █ φF) γ(B)γ(F) are given.

AMS Mathematics Subject Classification

05C69 05C62 

Key words and phrases

Graph bundle dominating set domination number Cartesian product 


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Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of MariborMariborSlovenia
  2. 2.FME (FS)Maribor
  3. 3.IMFMLjubljana

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