q-Coverings, codes, and line graphs

AbstractIn this paper we consider the relationship between q-coverings of a regular graph and perfect 1-codes in line graphs. An infinite class of perfect 1-codes in the line graphs L(Ik) is constructed

On perfect codes in Cartesian products of graphs

AbstractAssuming the existence of a partition in perfect codes of the vertex set of a finite or infinite bipartite graph G we give the construction of a perfect code in the Cartesian product G□G□P2. Such a partition is easily obtained in the case of perfect codes in Abelian Cayley graphs and we give some examples of applications of this result and its generalizations

Antipodal Distance Transitive Covers of Complete Graphs

AbstractA distance-transitive antipodal cover of a complete graphKnpossesses an automorphism group that acts 2-transitively on the fibres. The classification of finite simple groups implies a classification of finite 2-transitive permutation groups, and this allows us to determine all possibilities for such a graph. Several new infinite families of distance-transitive graphs are constructed