Undirected endo-Cayley digraphs of cyclic groups of order power of prime numbers. (3rd March 2016) - Promsakon, C.
Abstract: Let G be a finite group, A a subset of G and f an endomorphism on G . The endo-Cayley digraph of G corresponding to a connecting set A and an endomorphism f, denoted by endo – Cay f ( G, A )is a digraph whose vertex set is G and a vertex u is adjacent to vertex n if and only if v = f ( u ) a for some a ϵ A . In this paper, we focus on endo-Cayley graph of a ring of integer order power of prime numbers, ℤ p k when a connecting set is a set of all units in ℤ p k, denoted by U p k . We find conditions for an endomorphism on ℤ p k to make endo-Cayley digraphs of ℤ p k to be undirected graphs.