| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 106 === Let G=(V,E) be a simple graph.
A k-factor of G is a spanning subgraph of G such that each vertex is of degree k.
Two graphs G_1 and G_2 are isomorphic if there exists a bijection f:V(G_1) \rightarrow V(G_2) such that
{u, v} is an edge of G_1 if and only if {f(u), f(v)} is an edge of G_2.
If G_1 and G_2 are not isomorphic, then we say G_1 and G_2 are non-isomorphic graphs.
The well-known Petersen's theorem shows that every 2r-regular graph can be decomposed into r 2-factors.
Therefore, either K_{2n,2n} or K_{2n+1,2n+1}-I can be decomposed into n 2-factors.
In this thesis, we shall prove that not only the decomposition into 2-factors is possible,
but also we can decompose balanced complete bipartite graphs into non-isomorphic 2-factors.
The main tool we use is a newly defined notion called ``double Latin squares''.
As a consequence of our study,
we can also decompose the above mentioned graphs into isomorphic 2-factors for certain prescribed types of 2-factors.
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