A General Computational Tool for Structure 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.
Advisor:Takaya, Kunio; Dolovich, Allan T.; Burton, Richard T.; Zhang, W. J. (Chris)
School:University of Saskatchewan
School Location:Canada - Saskatchewan
Source Type:Master's Thesis
Keywords:structure synthesis graph isomorphism automorphism eigenvector eigenvalue canonical labeling
Date of Publication:11/05/2008