Algebraic graph theory

A highly symmetrical graph, the Petersen graph, which is vertex-transitive, symmetric, distance-transitive, and distance-regular. It has diameter 2. Its automorphism group has 120 elements, and is in fact the symmetric group .

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.