On digital H-spaces

We investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP₁ and NP₂ product adjacencies. We explore algebraic properties of digital H-spaces preserved under digital homotopy equivalence, and we give a general construction that produces examples of digital H-spaces that are not homotopy-equivalent to digital topological groups in both categories. Further, we show that this construction essentially classifies all NP₂-digital H-spaces. In a short appendix, we resolve a question that was left unresolved in [16], and complete the full classification of digital topological groups.