On forcibly k-connected and forcibly k-arc-connected digraphic sequences

For nonnegative integer sequences and , we say that majorizes , denoted by , if and for . A digraphic sequence is forcibly -connected (resp., -arc-connected) if each digraph with degree sequence is -connected (resp., -arc-connected). We give a sufficient condition for forcibly -connected (resp., -arc-connected) digraphic sequences and observe that if a digraphic sequence satisfies the condition (which implies is forcibly -connected (resp., -arc-connected)) then every digraphic sequence also satisfies the condition. If violates the condition, then we may take a sequence such that there exists a non--connected (resp., non--arc-connected) -realization.