Quadratic modulo 2n Cayley graphs Original Research Article

A family of simple, finite, undirected and without loops Cayley graphs Cay (Z2n,QR∗(2n)) is studied, where Z2n denotes the additive group of integers modulo 2n and the set S∗=S∪{−S}, where S=QR∗(2n) denotes the set of quadratic residues of Z2n, zero excluded. In this paper we show that the diameter of the Cayley graphs Cay (Z2n,QR∗(2n)) is 2 and we give recursive formulae for the number of triangles in the graph. In addition, we discuss the number of k-residues modulo pn, p prime and n⩾1.