Monthly notes from reading Norman Biggs's 'Algebraic Graph Theory', covering topics including vertex and edge transitivity, graph automorphisms, symmetric graphs, arc-transitivity, and related theorems. Key topics include: degrees of vertices in orbits, examples of regular non-vertex-transitive graphs (Frucht and Folkman graphs), the distinction between vertex-transitive and edge-transitive graphs, Frucht's 1938 theorem on automorphism groups, and the formal definition of symmetric (1-arc-transitive) graphs versus asymmetric graphs.
Table of contents
ContentsDegree of Vertices in an OrbitRegular Non-Vertex-Transitive GraphsVertex-Transitive But Not Edge-TransitiveEdge-Transitivex But Not Vertex-TransitiveBipartiteness as a Necessary ConditionGraph with an Automorphism GroupPermutation Groups Need Not Be Automorphism GroupsSymmetric GraphsSort: