Smarandachely antipodal signed digraphs

A Smarandachely k-signed digraph (Smarandachely k-marked digraph) is an ordered pair S = (D,[sigma]) (S = (D,[mu])) where D = (V, A) is a digraph called underlying digraph of S and a : A [right arrow] ([bar.e].sub.1], [bar.e].sub.2], ..., [bar.e].sub.k]) ([mu]: V [right arrow] ([bar.e].sub.1], [bar.e].sub.2], ..., [bar.e].sub.k])) is a function, where each [bar.e].sub.i] [member of] {+, -}. Particularly, a Smarandachely 2-signed digraph or Smarandachely 2-marked digraph is called abbreviated a signed digraph or a marked digraph. In this paper, we Define the Smarandachely antipodal signed digraph [??] (D) of a given signed digraph S = (D,[sigma]) and offer a structural characterization of antipodal signed digraphs. Further, we characterize signed digraphs S for which S ~ [??] (S) and [bar.S] ~ [??] (S) where ~ denotes switching equivalence and [??] (S) and [bar.S] are denotes the Smarandachely antipodal signed digraph and complementary signed digraph of S respectively.