UBC Theses and Dissertations
On the minimal polynomial and authomorpism group of a graph Ng, Fat-Kwong Louis
This thesis discusses the use of the characteristic polynomial and minimal polynomial of the adjacency matrix of a graph to characterize its automorphism group. We first consider the reducibility of the minimal polynomial of a graph and see how this reflects the properties of the graph and its automorphism group. Then we study the relationship between the number of orbits of a subgroup of the automorphism group of a graph and the factorization of its characteristic polynomial. Finally we present an algorithm to determine the automorphism partitioning of a graph using its characteristic polynomial. Most of the results can also be extended to directed graphs and to graphs with parallel edges and loops.
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