Summary: We give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph \(G_{k}\)-with some \(k\)-adjacency in \(\mathbb{Z}^n\) can be recognized by the simplicial complex spanned by \(G_k\). Moreover, we demonstrate that a graphically \((k_0 k_1)\)-continuous map \(f: {sl G}_{k_0} \subset \mathbb{Z}^{n_0} \to G_{k_1} \subset \mathbb{Z}^{n_1}\) can be converted into the simplicial map \(S(f) : S(G_{k_0}) \to S(G_{k_1})\) with relation to combinatorial topology. Finally, if \(G_{k_0}\) is not \((k_0,3^{n_0}- 1)\)-homotopy equivalent to \(SC^{n_0,4}_{3^{n_0}-1}\), a graphically \((k_0, k_1)\)-continuous map (respectively a graphically \((k_0,k_1)\)-isomorphism) \(f: G_{k_0} \subset \mathbb{Z}^{n_0} \to G_{k_1} \subset \mathbb{Z}^{n_1}\) induces the group homomorphism (respectively the group isomorphism) \(S(f)_* : \pi_1(S(G_{k_0}),u_0) \to pi_1(S(G_{k_1}),f(u_0))\) in algebraic topology.