On The Unit Dot Product Graph Of A Commutative Ring.
A Master of Science thesis in Mathematics by Mohammad Ahmad Abdulla entitled, "On The Unit Dot Product Graph Of A Commutative Ring," submitted in January 2016. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available.
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| Format: | doctoralThesis |
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2016
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| Online Access: | http://hdl.handle.net/11073/8319 |
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| _version_ | 1864513437154934784 |
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| author | Abdulla, Mohammad Ahmad |
| author_facet | Abdulla, Mohammad Ahmad |
| author_role | author |
| dc.contributor.none.fl_str_mv | Badawi, Ayman |
| dc.creator.none.fl_str_mv | Abdulla, Mohammad Ahmad |
| dc.date.none.fl_str_mv | 2016-05-11T09:06:40Z 2016-05-11T09:06:40Z 2016-01 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2016.02 http://hdl.handle.net/11073/8319 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Total dot product graphs zero dot product graphs dominating sets domination number Commutative rings |
| dc.title.none.fl_str_mv | On The Unit Dot Product Graph Of A Commutative Ring. |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Mohammad Ahmad Abdulla entitled, "On The Unit Dot Product Graph Of A Commutative Ring," submitted in January 2016. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available. |
| format | doctoralThesis |
| id | aus_6ee41955955cf3e29a9f9a4f0c6784fb |
| identifier_str_mv | 29.232-2016.02 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/8319 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | On The Unit Dot Product Graph Of A Commutative Ring.Abdulla, Mohammad AhmadTotal dot product graphszero dot product graphsdominating setsdomination numberCommutative ringsA Master of Science thesis in Mathematics by Mohammad Ahmad Abdulla entitled, "On The Unit Dot Product Graph Of A Commutative Ring," submitted in January 2016. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available.In 2015, Ayman Badawi (Badawi, 2015) introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 n < 1 be an integer, and R =A x A x ... x A (n times). We recall from (Badawi, 2015) that total dot product graph of R is the (undirected) graph TD(R) with vertices R* = R \ {(0, 0, ..., 0)}, and two distinct vertices x and y are adjacent if and only if xy = 0 [is an element of] A (where xy denote the normal dot product of x and y). Let Z(R) denotes the set of all zero-divisors of R. Then the zero-divisor dot product graph of R is the induced subgraph ZD(R) of TD(R) with vertices Z(R) = Z(R)* \ {(0, 0, ..., 0)}. Let U(R) denotes the set of all units of R. Then the unit dot product graph of R is the induced subgraph UD(R) of TD(R) with vertices U(R). Let n 2 and A = Zn. The main goal of this thesis is to study the structure of UD(R = A x A).College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Badawi, Ayman2016-05-11T09:06:40Z2016-05-11T09:06:40Z2016-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2016.02http://hdl.handle.net/11073/8319en_USoai:repository.aus.edu:11073/83192025-06-26T12:20:24Z |
| spellingShingle | On The Unit Dot Product Graph Of A Commutative Ring. Abdulla, Mohammad Ahmad Total dot product graphs zero dot product graphs dominating sets domination number Commutative rings |
| status_str | publishedVersion |
| title | On The Unit Dot Product Graph Of A Commutative Ring. |
| title_full | On The Unit Dot Product Graph Of A Commutative Ring. |
| title_fullStr | On The Unit Dot Product Graph Of A Commutative Ring. |
| title_full_unstemmed | On The Unit Dot Product Graph Of A Commutative Ring. |
| title_short | On The Unit Dot Product Graph Of A Commutative Ring. |
| title_sort | On The Unit Dot Product Graph Of A Commutative Ring. |
| topic | Total dot product graphs zero dot product graphs dominating sets domination number Commutative rings |
| url | http://hdl.handle.net/11073/8319 |