Smarandachely antipodal signed digraphs

Abstract A Smarandachely k-signed digraph (Smarandachely k-marked digraph) is an or-dered pair S = (D,σ) (S = (D,µ)) where D = (V,A) is a digraph called underlying digraph of S and σ: A → (e1, e2,..., ek) (µ: V → (e1, e2,..., ek)) is a function, where each ei ∈ {+,−}. 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 A (D) of a given signed digraph S = (D,σ) and offer a structural characterization of antipodal signed digraphs. Further, we characterize signed digraphs S for which S ∼ −→A (S) and S ∼ −→A (S) where ∼ denotes switching equivalence and −→A (S) and S are denotes the Smarandachely antipodal signed digraph and complementary signed digraph of S respectively