Prime cubic order Cayley graphs over cyclic groups

We investigate the cubic Cayley graph [Formula: see text] of cyclic group [Formula: see text] of order [Formula: see text], where [Formula: see text] and [Formula: see text] are two distinct prime numbers and [Formula: see text] consists of all elements in [Formula: see text] of order [Formula: see text] or [Formula: see text]. We present some characteristics of [Formula: see text] including its connectivity, diameter, regularity, Eulerianity, girth, and Hamiltonicity. We show that the graph is Eulerian and has girth 3, and prove that the Cayley graph is a Hamiltonian or a semi-Hamiltonian graph. Furthermore we discuss the independence, chromatic, clique and domination numbers of the graph.