In tropical algebras we substitute min or max for the typical addition and then substitute addition for multiplication. A dot product representation of a graph assigns each vertex of the graph a vector such that two edges are adjacent if and only if the dot product of their vectors is greater than some chosen threshold. The resultS of creating dot product representations of graphs using tropical algebras are examined. In particular we examine the tropical dot product dimensions of graphs and establish connections to threshold graphs and the threshold dimension of a graph.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-5499 |
| Date | 01 May 2015 |
| Creators | Turner, Nicole |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). |
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