Strong homotopy induced by adjacency structure (Q2092351)

The paper under review deals with some thinning of a graph using a strong \(SA\)-deformation retract of a simple graph compared to a strong \(SA\)-homotopic thinning. Besides, the paper proves that two simple graphs are \(SA\)-homotopy equivalent iff they have graph isomorpic cores. In addition, the mapping class group of a graph is introduced and studied. However, since the notion of an \(SA\)-homotopy equivalence on an adjacency-based graph induced by an Alexandroff space is so rigid, we have some limitations of its use in applied sciences or digital geometry.