2026-09-20T14:35:24.433585600Zhttps://opus.uleth.ca/server/oai/request
oai:opus.uleth.ca:10133/6322019-02-08T06:07:13Zcom_10133_3346com_10133_1com_10133_296col_10133_3347col_10133_298
ULethbridge OPUS Repository supervisor Wismath, Stephen supervisor Gaur, Daya author Nickle, Elspeth J. author University of Lethbridge. Faculty of Arts and Science 2008-04-03T20:39:49Z 2008-04-03T20:39:49Z 2005 https://hdl.handle.net/10133/632 A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar. en_US Graph theory Computer graphics Geometrical constructions Graphic methods Dissertations, Academic Classes of arrangement graphs in three dimensions Thesis TGljZW5zZSBncmFudGVkIGJ5IEpha2UgQ2FtZXJvbiAoamFjb2IuY2FtZXJvbkB1bGV0aC5jYSkgb24gMjAwOC0wNC0wM1QyMDozMzowOVogKEdNVCk6Cgo8cD5OT04tRVhDTFVTSVZFIERJU1RSSUJVVElPTiBMSUNFTlNFPGJyIC8+CgpCeSBzaWduaW5nIGFuZCBzdWJtaXR0aW5nIHRoaXMgbGljZW5zZSwgeW91ICh0aGUgYXV0aG9yKHMpIG9yPGJyIC8+Y29weXJpZ2h0IG93bmVyKHMpKSBncmFudCB0byB0aGUgVW5pdmVyc2l0eSBvZiBMZXRoYnJpZGdlIChVIG9mIEwpPGJyIC8+dGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgdG8gcmVwcm9kdWNlLCB0cmFuc2xhdGUgKGFzIGRlZmluZWQ8YnIgLz5iZWxvdyksIGFuZC9vciBkaXN0cmlidXRlIHlvdXIgc3VibWlzc2lvbiAoaW5jbHVkaW5nIHRoZSBhYnN0cmFjdCk8YnIgLz53b3JsZHdpZGUgaW4gcHJpbnQgYW5kIGVsZWN0cm9uaWMgZm9ybWF0IGFuZCBpbiBhbnk8YnIgLz5tZWRpdW0sIGluY2x1ZGluZyBidXQgbm90IGxpbWl0ZWQgdG8gYXVkaW8gb3IgdmlkZW8uPGJyIC8+CgpZb3UgYWdyZWUgdGhhdCBVIG9mIEwgbWF5LCB3aXRob3V0IGNoYW5naW5nIHRoZSBjb250ZW50LCB0cmFuc2xhdGU8YnIgLz50aGUgc3VibWlzc2lvbiB0byBhbnkgbWVkaXVtIG9yIGZvcm1hdCBmb3IgdGhlIHB1cnBvc2U8YnIgLz5vZiBwcmVzZXJ2YXRpb24uPGJyIC8+CgpZb3UgYWxzbyBhZ3JlZSB0aGF0IFUgb2YgTCBtYXkga2VlcCBtb3JlIHRoYW4gb25lIGNvcHkgb2YgdGhpczxiciAvPnN1Ym1pc3Npb24gZm9yIHB1cnBvc2VzIG9mIHNlY3VyaXR5LCBiYWNrLXVwIGFuZCBwcmVzZXJ2YXRpb24uPGJyIC8+CgpZb3UgcmVwcmVzZW50IHRoYXQgdGhlIHN1Ym1pc3Npb24gaXMgeW91ciBvcmlnaW5hbCB3b3JrLCBhbmQgdGhhdDxiciAvPnlvdSBoYXZlIHRoZSByaWdodCB0byBncmFudCB0aGUgcmlnaHRzIGNvbnRhaW5lZCBpbiB0aGlzPGJyIC8+bGljZW5zZS4gWW91IGFsc28gcmVwcmVzZW50IHRoYXQgeW91ciBzdWJtaXNzaW9uIGRvZXMgbm90LCB0byB0aGU8YnIgLz5iZXN0IG9mIHlvdXIga25vd2xlZGdlLCBpbmZyaW5nZSB1cG9uIGFueW9uZSdzIGNvcHlyaWdodC48YnIgLz4KCklmIHRoZSBzdWJtaXNzaW9uIGNvbnRhaW5zIG1hdGVyaWFsIGZvciB3aGljaCB5b3UgZG8gbm90IGhvbGQ8YnIgLz5jb3B5cmlnaHQsIHlvdSByZXByZXNlbnQgdGhhdCB5b3UgaGF2ZSBvYnRhaW5lZCB0aGUgdW5yZXN0cmljdGVkPGJyIC8+cGVybWlzc2lvbiBvZiB0aGUgY29weXJpZ2h0IG93bmVyIHRvIGdyYW50IFUgb2YgTCB0aGUgcmlnaHRzPGJyIC8+cmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdCBzdWNoIHRoaXJkLXBhcnR5IG93bmVkIG1hdGVyaWFsPGJyIC8+aXMgY2xlYXJseSBpZGVudGlmaWVkIGFuZCBhY2tub3dsZWRnZWQgd2l0aGluIHRoZSB0ZXh0PGJyIC8+b3IgY29udGVudCBvZiB0aGUgc3VibWlzc2lvbi48YnIgLz4KCklGIFRIRSBTVUJNSVNTSU9OIElTIEJBU0VEIFVQT04gV09SSyBUSEFUIEhBUyBCRUVOIFNQT05TT1JFRCBPUjxiciAvPlNVUFBPUlRFRCBCWSBBTiBBR0VOQ1kgT1IgT1JHQU5JWkFUSU9OIE9USEVSIFRIQU4gVSBvZiBMIFlPVTxiciAvPlJFUFJFU0VOVCBUSEFUIFlPVSBIQVZFIEZVTEZJTExFRCBBTlkgUklHSFQgT0YgUkVWSUVXIE9SIE9USEVSPGJyIC8+T0JMSUdBVElPTlMgUkVRVUlSRUQgQlkgU1VDSCBDT05UUkFDVCBPUiBBR1JFRU1FTlQuPGJyIC8+CgpVIG9mIEwgd2lsbCBjbGVhcmx5IGlkZW50aWZ5IHlvdXIgbmFtZShzKSBhcyB0aGUgYXV0aG9yKHMpIG9yPGJyIC8+b3duZXIocykgb2YgdGhlIHN1Ym1pc3Npb24sIGFuZCB3aWxsIG5vdCBtYWtlIGFueSBhbHRlcmF0aW9uLCBvdGhlcjxiciAvPnRoYW4gYXMgYWxsb3dlZCBieSB0aGlzIGxpY2Vuc2UsIHRvIHlvdXIgc3VibWlzc2lvbi48L3A+Cg== URL http://localhost:4000/bitstreams/7cc5827b-815a-4fcb-b8b4-3f8bf4e1b65e/download File MD5 424a9f668812cdeaf5c9a6d7f189a45c 7147981 application/pdf NICKLE_ELSPETH_MSC_2005.pdf URL http://localhost:4000/bitstreams/1e4d4c1f-2fc9-42ce-9d7e-7070c347ca74/download File MD5 8b4c45b5107dbdaf37a08d15b60ab828 150675 text/plain NICKLE_ELSPETH_MSC_2005.pdf.txt