Inequalities involving the irredundance number of a graph

The chain of inequalities IR(G)⩽WP(G¯)⩽v+1-WP(G)⩽v+1-SW(G)⩽v-δ(G) is proved, where IR(G), WP(G) and SW(G) denote the irredundance number, Welsh-Powell invariant and Szekeres-Wilf invariant of G, respectively.