ON THE SIMPLICIAL COMPLEX STEMMED FROM A

Abstract. In this paper, we give a digital graph-theoretical ap-proach of the study of digital images with relation to a simpli-cial complex. Thus, a digital graph Gk with some k-adjacency in Zn can be recognized by the simplicial complex spanned by Gk. Moreover, we demonstrate that a graphically (k0, k1)-continuous map f: Gk0 ⊂ Zn0 → Gk1 ⊂ Zn1 can be converted into the simplicial map S(f) : S(Gk0) → S(Gk1) with relation to combi-natorial topology. Finally, if Gk0 is not (k0, 3 n0 − 1)-homotopy equivalent to SCn0,43n0−1, a graphically (k0, k1)-continuous map (re-spectively a graphically (k0, k1)-isomorphisim) f: Gk0 ⊂ Zn0 → Gk1 ⊂ Zn1 induces the group homomorphism (respectively the group isomorphisim)S(f) ∗ : pi1(S(Gk0), v0) → pi1(S(Gk1), f(v0)) in algebraic topology. 1