Undirected endo-Cayley digraphs of cyclic groups of order power of prime numbers. (3rd March 2016)

• Record Type: Journal Article
• Authors: Promsakon, C.
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 19:Number 2(2016)
• Page Start: 321
• Page End: 330
• Publication Date: 2016-03-03
• Subjects: endo-Cayley graphs -- undirected graphs -- cyclic groups; 46MO5 -- 05C40 -- 05C76; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2015.1086064
• Languages: English
• ISSNs: 0972-0529

Abstract

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.