Cayley Graphs Versus Algebraic Graphs

Abstract

Let Γ be a finite group and let S ⊆ Γ be a subset. The Cayley graph, denoted byCay(Γ, S) has vertex set Γ and two distinct vertices x, y ∈ Γ are joined by a directed edge fromx to y if and only if there exists s ∈ S such that x = sy. In this manuscript, we characterize the generating setsS for which Cay(Γ, S) is isomorphic to somealgebraic graphs, namely, unit graphs, co-unit graphs, total graph and co-total graphs.