Irredundance in inflated graphs

  • Authors:

  • Odile Favaron

  • Affiliations:

  • LRI, Bat. 490, Université de Paris-Sud, 91405 Orsay cedex, France

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 1998

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Abstract

The inflation GI of a graph G withn(G) vertices and m(G) edges isobtained by replacing every vertex of degree d of Gby a clique Kd. We study the lower and upperirredundance parameters ir and IR of an inflation. Weprove in particular that if γ denotes the domination numberof a graph, γ(GI) -ir(GI) can be arbitrarily large,IR(GI) ≤ m(G) andIR(GI) ≤n2(G)-4. These results disprove aconjecture of Dunbar and Haynes (Congr. Num. 118(1996), 143154) and answer another open question. © 1998 JohnWiley & Sons, Inc. J Graph Theory 28: 97104, 1998