Dec 3, 2025 · A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element …

Jun 13, 2025 · A vertex-transitive graph is a graph where the automorphism group acts transitively on its vertices. In simpler terms, it's a graph where every vertex has the same "local …

A graph X is vertex transitive (or just transitive) if its automorphism group acts transitively on V(X). Thus for any two distinct vertices of X there is an automorphism mapping one to the other.

Problem 1.4. Determine the connected 4-valent arc-transitive graphs and the connected 3-valent vertex-transitive graphs admitting an automorphism fixing precisely 1/3 of the vertices.

Theorem 2 (Babai Szegedy) If G is vertex transitive and X V (G) with diam(X) < diam(G) then j@(X)j 1 jXj diam(X) + 1 s number is the same for any two vertices). Let P denot the set of …

Vertex-transitive refers to a property of a graph where for any pair of vertices, there exists an automorphism of the graph that maps one vertex to the other. This means that the …

If for any pair of vertices u and v in a graph, there is an automorphism mapping u to v, then the graph is said to be vertex transitive and has the interesting property that it "looks the...

In this paper we consider transitive permutation groups of degree mn generated by a “rotation” ρ which is a product of m disjoint cycles of length n and by a “twisted translation” t; such that τρτ …

May 1, 2024 · In this paper we investigate orders, longest cycles and the number of cycles of automorphisms of finite vertex-transitive graphs. In particular, we show that the order of every …

The edges of the truncated tetrahedron form a vertex-transitive graph (also a Cayley graph) which is not symmetric. Finite vertex-transitive graphs include the symmetric graphs (such as the …