Torsion in the magnitude homology of graphs

Magnitude homology is a bigraded theory for finite graphs defined by Hepworth and Willerton, categorifying the power series invariant known as magnitude which was introduced Leinster. We analyze structure implications of torsion in homology. show that any finitely generated abelian group may appear subgroup graph, and, particular, given prime order can graph there are infinitely many such graphs. Finally, we provide complete computations class outerplanar focus on ranks groups along main diagonal