43 research outputs found
On the Weisfeiler-Leman dimension of some polyhedral graphs
Let be a positive integer, a graph with vertex set , and
the coloring of the Cartesian -power , obtained by
the -dimensional Weisfeiler-Leman algorithm. The -dimension of the
graph is defined to be the smallest for which the coloring determines up to isomorphism. It is known that the -dimension of any planar graph is or , but no planar graph of -dimension is known. We prove that the -dimension of a
polyhedral (i.e., -connected planar) graph is at most if the color
classes of the coloring are the orbits of the componentwise
action of the group on