Lang, Julie2014-08-182014-08-182014-08-18http://hdl.handle.net/2097/18260A (1, ≤ 2)-identifying code is a subset of the vertex set C of a graph such that each pair of vertices intersects C in a distinct way. This has useful applications in locating errors in multiprocessor networks and threat monitoring. At the time of writing, there is no simply-stated rule that will indicate if a graph is (1, ≤ 2)-identifiable. As such, we discuss properties that must be satisfied by a valid (1, ≤ 2)-identifying code, characteristics of a graph which preclude the existence of a (1, ≤ 2)-identifying code, and relationships between the maximum degree and order of (1, ≤ 2)-identifiable graphs. Additionally, we show that (1, ≤ 2)-identifiable graphs have no forbidden induced subgraphs and provide a list of (1, ≤ 2)-identifiable graphs with minimum (1, ≤ 2)-identifying codes indicated.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Identifying codesGraph theoryDominating setsThesisMathematics (0405)