Perfect codes and regular partitions in graphs and groups (Q580375)

The author's abstract states: ``We define the concept of regular partition of a graph \(\Gamma\) and its relationship to the automorphism group of \(\Gamma\). In application, we give necessary conditions for a perfect code of \(\Gamma\) in the sense of Biggs to exist. We recover a theorem of C. Landauer relating perfect codes in a finite group to its characters. We establish a necessary condition on the subgroups for the existence of a perfect code. As an application, we mention a result of O. Rothaus and J. G. Thompson concerning the existence of perfect codes in permutation groups.''