The direct expansion of graphs Original Research Article

The concept of expansion of a graph has proved to be an efficient tool in the study of median, quasi-median and partial Hamming graphs. The basic idea of expansion is that given a graph G, we obtain a graph G′ by enlarging a subgraph of G according to a certain rule in such a way that G′ inherits certain properties of G. Mulder suggested several new rules for such expansions (H.M. Mulder, The expansion procedure for graphs, in: R. Bodendiek (Ed.), Contemporary Methods in Graph Theory, B.I.-Wissenschaftsverlag, Manhaim, 1990, pp. 459–477). In particular he pointed out the case when a direct product in the process of expansion is used, and called it a relational expansion. In this paper we investigate it in further detail, especially, we deal with preservation of connectivity by this expansion.