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dc.contributor.advisorZhang, W. J. (Chris)en_US
dc.creatorHe, Peirenen_US
dc.date.accessioned2008-10-06T10:43:05Zen_US
dc.date.accessioned2013-01-04T05:00:36Z
dc.date.available2009-11-05T08:00:00Zen_US
dc.date.available2013-01-04T05:00:36Z
dc.date.created2003-10en_US
dc.date.issued2003-10en_US
dc.date.submittedOctober 2003en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-10062008-104305en_US
dc.description.abstractSynthesis of structures is a very difficult task even with only a small number of components that form a system; yet it is the catalyst of innovation. Molecular structures and nanostructures typically have a large number of similar components but different connections, which manifests a more challenging task for their synthesis. This thesis presents a novel method and its related algorithms and computer programs for the synthesis of structures. This novel method is based on several concepts: (1) the structure is represented by a graph and further by the adjacency matrix; and (2) instead of only exploiting the eigenvalue of the adjacency matrix, both the eigenvalue and the eigenvector are exploited; specifically the components of the eigenvector have been found very useful in algorithm development. This novel method is called the Eigensystem method. The complexity of the Eigensystem method is equal to that of the famous program called Nauty in the combinatorial world. However, the Eigensystem method can work for the weighted and both directed and undirected graph, while the Nauty program can only work for the non-weighted and both directed and undirected graph. The cause for this is the different philosophies underlying these two methods. The Nauty program is based on the recursive component decomposition strategy, which could involve some unmanageable complexities when dealing with the weighted graph, albeit no such an attempt has been reported in the literature. It is noted that in practical applications of structure synthesis, weighted graphs are more useful than non-weighted graphs for representing physical systems. Pivoted at the Eigensystem method, this thesis presents the algorithms and computer programs for the three fundamental problems in structure synthesis, namely the isomorphism/automorphism, the unique labeling, and the enumeration of the structures or graphs.en_US
dc.language.isoen_USen_US
dc.subjectstructure synthesisen_US
dc.subjectgraph isomorphismen_US
dc.subjectgraph automorphismen_US
dc.subjecteigenvectoren_US
dc.subjecteigenvalueen_US
dc.subjectcanonical labelingen_US
dc.titleA general computational tool for structure synthesisen_US
thesis.degree.departmentMechanical Engineeringen_US
thesis.degree.disciplineMechanical Engineeringen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberTakaya, Kunioen_US
dc.contributor.committeeMemberDolovich, Allan T.en_US
dc.contributor.committeeMemberBurton, Richard T.en_US


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