Representative results :

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1. The complete classification of finite primitive permutation groups containing an abelian regular subgroup, by Li, solved a long-standing open problem initiated by Burnside in 1900, and now is an important tool in the study of Cayley graphs of abelian groups.

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2. The complete classification of vertex-primitive and biprimitive s-arc transitive graphs for s>3 , by Li, generated new constructions of 4-arc-transitive graphs; in particular, discovered a unique vertex-primitive 4-arc-transitive graph representation for the Monster simple group, and solved a conjecture of Biggs and Hoare (1983).

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3. The comprehensive investigation of the isomorphism problem for Cayley graphs in Li's PhD thesis (1997), solved a series of important problems regarding Cayley graphs, and in particular, proved that finite CI-groups are soluble, which completed and improved the work of Babai and Frankel dating from 1978.

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4. The theory of edge-transitive Cayley graphs, developed by Li, is powerful; led to the proof that there exist only finitely many basic 3-arc transitive Cayley graphs of any given valency, the classification of regular Cayley maps of simple groups, the construction of counter-examples to the question of Wielandt (1964) regarding Burnside groups.

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5. The introduction and the theory of homogeneous factorisations of graphs, by Li and Praeger, discovered a type of important combinatorial structure, developed a powerful method for studying factorisations of symmetrical graphs, and answered the long-standing open question regarding the existence of vertex-transitive self-complementary non-Cayley graphs.

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