Difference divisor graph of the finite group

Let (Zn, +) be a finite group of integers modulo n and Dn a non-empty subset of Zn containing proper devisors of n. In this paper, we have introduced the difference divisor graph Diff (Zn, Dn) associated with Zn whose vertices coincide with Zn such that two distinct vertices are adjacent if and only...

Full description

Bibliographic Details
Main Authors: R. V M S S Kiran Kumar, T. Chalapathi
Format: Article
Language:English
Published: Ayandegan Institute of Higher Education, 2018-09-01
Series:International Journal of Research in Industrial Engineering
Subjects:
Online Access:http://www.riejournal.com/article_69250_1d00716160a19ba1d9e33ac758593c00.pdf
_version_ 1818730046455545856
author R. V M S S Kiran Kumar
T. Chalapathi
author_facet R. V M S S Kiran Kumar
T. Chalapathi
author_sort R. V M S S Kiran Kumar
collection DOAJ
description Let (Zn, +) be a finite group of integers modulo n and Dn a non-empty subset of Zn containing proper devisors of n. In this paper, we have introduced the difference divisor graph Diff (Zn, Dn) associated with Zn whose vertices coincide with Zn such that two distinct vertices are adjacent if and only if either a-b belongs to Dn or b-a belongs to Dn . We have investigated its algebraic and graph theoretic properties. Further, we have proved that the difference divisor graph Diff (Zn, Dn) is not a Cayley graph.
first_indexed 2024-12-17T22:55:33Z
format Article
id doaj.art-0380b69cce394033bd35abd39456c300
institution Directory Open Access Journal
issn 2783-1337
2717-2937
language English
last_indexed 2024-12-17T22:55:33Z
publishDate 2018-09-01
publisher Ayandegan Institute of Higher Education,
record_format Article
series International Journal of Research in Industrial Engineering
spelling doaj.art-0380b69cce394033bd35abd39456c3002022-12-21T21:29:33ZengAyandegan Institute of Higher Education,International Journal of Research in Industrial Engineering2783-13372717-29372018-09-017223524210.22105/riej.2018.133136.104269250Difference divisor graph of the finite groupR. V M S S Kiran Kumar0T. Chalapathi1Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati, -517502, Andhra Pradesh, India.Department of Mathematics, S. V. University, Tirupati, -517502, Andhra Pradesh, India.Let (Zn, +) be a finite group of integers modulo n and Dn a non-empty subset of Zn containing proper devisors of n. In this paper, we have introduced the difference divisor graph Diff (Zn, Dn) associated with Zn whose vertices coincide with Zn such that two distinct vertices are adjacent if and only if either a-b belongs to Dn or b-a belongs to Dn . We have investigated its algebraic and graph theoretic properties. Further, we have proved that the difference divisor graph Diff (Zn, Dn) is not a Cayley graph.http://www.riejournal.com/article_69250_1d00716160a19ba1d9e33ac758593c00.pdfdivisor graphdifference divisor graphhamilton cyclegcd-graphcayley graph
spellingShingle R. V M S S Kiran Kumar
T. Chalapathi
Difference divisor graph of the finite group
International Journal of Research in Industrial Engineering
divisor graph
difference divisor graph
hamilton cycle
gcd-graph
cayley graph
title Difference divisor graph of the finite group
title_full Difference divisor graph of the finite group
title_fullStr Difference divisor graph of the finite group
title_full_unstemmed Difference divisor graph of the finite group
title_short Difference divisor graph of the finite group
title_sort difference divisor graph of the finite group
topic divisor graph
difference divisor graph
hamilton cycle
gcd-graph
cayley graph
url http://www.riejournal.com/article_69250_1d00716160a19ba1d9e33ac758593c00.pdf
work_keys_str_mv AT rvmsskirankumar differencedivisorgraphofthefinitegroup
AT tchalapathi differencedivisorgraphofthefinitegroup