The Reduced Smith Group of a Kneser Graph and Its Application to Group-Valued Magic Maps

For a finite abelian group $Γ$, a map $f\colon V(G)\toΓ$ is a $Γ$-magic map if the sum of its values over the neighbors of a vertex is independent of the vertex. It is affinely generating if its pairwise differences generate $Γ$. When $|Γ|=|V(G)|$, a bijective $Γ$-magic map is a $Γ$-distance magic l