D-magic strongly regular graphs

Abstract

For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x. In this paper we utilize spectra of graphs to characterize strongly regular graphs which are D-magic, for all possible distance sets D. In addition, we provide necessary conditions for distance regular graphs of diameter 3 to be {1}-magic.