page_title: Zero-symmetric graph
hierarchical_section_title: Zero-symmetric graph
context_page_description: In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for each two vertices, there is a unique symmetry taking one vertex to the other. Such a graph is a vertex-transitive graph but cannot be an edge-transitive graph: the number of symmetries equals the number of vertices, too few to take every edge to every other edge.
  The name for this class of graphs was coined by R. M. Foster in a 1966 letter to H. S. M. Coxeter. These graphs are nowadays referred to as cubic GRR.
context_section_description: In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for each two vertices, there is a unique symmetry taking one vertex to the other. Such a graph is a vertex-transitive graph but cannot be an edge-transitive graph: the number of symmetries equals the number of vertices, too few to take every edge to every other edge.
  The name for this class of graphs was coined by R. M. Foster in a 1966 letter to  H. S. M. Coxeter. These graphs are nowadays referred to as cubic GRR (Graphical Regular Representations).
caption: The smallest zero-symmetric graph with two edge orbits