Independence and upper irredundance in claw-free graphs Original Research Article

It is known that the independence number of a connected claw-free graph G of order n is at most (n+1)/2. We improve this result by showing that this bound still holds for the upper irredundance number IR(G). We characterize the connected claw-free graphs for which IR(G)=(n+1)/2 and give some properties of those graphs for which IR(G)=n/2 if n is even or IR(G)=(n−1)/2 if n is odd.