Algebraic graph theory
![](/Images/godic/202412/18/Petersen1_tiny.svg1617.png")
![A Cayley graph for the alternating group A4, forming a truncated tetrahedron in three dimensions. All Cayley graphs are vertex-transitive, but some vertex-transitive graphs (like the Petersen graph) are not Cayley graphs.](/Images/godic/202412/18/TruncatedTetrahedron1617.gif")
![A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. According to the chromatic polynomial, there are 120 such colorings with 3 colors.](/Images/godic/202412/18/Petersen_graph_3-coloring.svg1617.png")
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.