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...
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Format: | Article |
Language: | English |
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Ayandegan Institute of Higher Education,
2018-09-01
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Series: | International Journal of Research in Industrial Engineering |
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Online Access: | http://www.riejournal.com/article_69250_1d00716160a19ba1d9e33ac758593c00.pdf |
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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. |
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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 |