A Generalization of Cayley Digraphs and Graphs

In this study, we present a new family of digraphs and graphs that can be considered as the generalization of the class of Cayley digraphs and graphs. For two subgroup L;R of group G and a subset S of G, we define double coset digraph Γ→ (G;L;R;S) to have vertex set of all double cosets of L;R in G, and an arc from LxR to LyR if and only if y = lsl′xr for some l; l′ ∈ L, s ∈ S and r ∈ R. We have expressed and obtained many properties related to these graphs.