Dissertation/Thesis Abstract

Determination of a Graph's Chromatic Number for Part Consolidation in Axiomatic Design
by Cavallaro, Jeffery A., M.S., San Jose State University, 2020, 161; 27836747
Abstract (Summary)

Mechanical engineering design practices are increasingly moving towards a framework called axiomatic design (AD). A key tenet of AD is to decrease the information content of a design in order to increase the chance of manufacturing success. An important way to decrease information content is to fulfill multiple functional requirements (FRs) by a single part: a process known as part consolidation. One possible method for determining the minimum number of required parts is to represent a design by a graph, where the vertices are the FRs and the edges represent the need to separate their endpoint FRs into separate parts. The answer is then the chromatic number of such a graph. This research investigates the suitability of using two existing algorithms and a new algorithm for finding the chromatic number of a graph in a part consolidation tool that can be used by designers. The runtime complexities and durations of the algorithms are compared empirically using the results from a random graph analysis with binomial edge probability. It was found that even though the algorithms are quite different, they all execute in the same amount of time and are suitable for use in the desired design tool.

Indexing (document details)
Advisor: Jahanbekam, Sogol
Commitee: So, Wasin, Schettler, Jordan
School: San Jose State University
Department: Mathematics
School Location: United States -- California
Source: MAI 82/1(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Axiomatic design, Chromatic number, Graph theory
Publication Number: 27836747
ISBN: 9798662400214
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