Cayley Graphs Versus Algebraic Graphs

Pranjali Pranjali (University of Rajasthan)
Amit Kumar (Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India.)
Tanuja Yadav (Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali-304022, India.)

Journal of the Indonesian Mathematical Society
VOLUME 27 NUMBER 2 (July 2021)

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.