Caro, Davila, and Pepper recently proved δ(G)α(G)≤Δ(G)μ(G) for every graph G with minimum degree δ(G), maximum Δ(G), independence number α(G), matching μ(G). Answering some problems they posed, we characterize the extremal graphs δ(G)<Δ(G) as well δ(G)=Δ(G)=3.