The Lower Domination Parameters in Inflation of Graphs of Radius 1

Abstract

The inflation GI of a graph G is the line graph of the subdivision of G. If G is a complete graph the equality ir(GI) = γ(GI) was proved by Favaron in 1998. We conjectured that the equality holds when G is any graph of radius 1. But it turned out that it is not true. Moreover, we proved that for the class of radius 1 graphs there does not exist a better upper bound for the relation γ(GI)/ir(G I) then 32. We found also a sufficient condition for the equality γ(GI)=ir(GI). © 2003 Elsevier B.V. All rights reserved.