Graph Isomorphism
نویسندگان
چکیده
While in general it is not known whether there is a polynomial time algorithm to decide whether two given graphs are isomorphic, there are polynomial-time algorithms for certain subsets of graphs, including but not limited to planar graphs and graphs with bounded valence. In this thesis, we will give a brief introduction on the Graph Isomorphism Problem and its relations to complexity theory. We show that permutation groups can, despite their large sizes, stored in digital computers in a succinct way. This raises questions about our ability to answer important questions about these permutation groups with algorithms in polynomial time. We present some polynomial-time algorithms that can determine basic facts about succinctly stored groups. After this, we proof that graphs with valence bounded by 3 can be checked for isomorphism in polynomial time, following the proof given by Luks [Luk82].
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