Graph families | Regular graphs | Algebraic graph theory

Half-transitive graph

In the mathematical field of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is half-transitive if its automorphism group acts transitively upon both its vertices and its edges, but not on ordered pairs of linked vertices. Every connected symmetric graph must be vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree, so that half-transitive graphs of odd degree do not exist. However, there do exist half-transitive graphs of even degree. The smallest half-transitive graph is the Holt graph, with degree 4 and 27 vertices. (Wikipedia).

Half-transitive graph
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Related pages

Graph theory | Vertex-transitive graph | Graph (discrete mathematics) | Automorphism group | Mathematics | Holt graph | Symmetric graph | Edge-transitive graph