Are regular graphs vertex-transitive?
All vertex-transitive graphs are regular, but not necessarily vice versa. A regular graph that is edge-transitive but not vertex-transitive is called a semisymmetric graph. In contrast, any graph that is both edge-transitive and vertex-transitive is called a symmetric graph (Holton and Sheehan 1993, pp. 209-210).
How do you determine if a graph is transitive?
An undirected graph has a transitive orientation if its edges can be oriented in such a way that if (x, y) and (y, z) are two edges in the resulting directed graph, there also exists an edge (x, z) in the resulting directed graph.
What does it mean for a graph to be transitive?
A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular.
Is a graph with no edges transitive?
Informally speaking, a graph is edge-transitive if every edge has the same local environment, so that no edge can be distinguished from any other based on the vertices and edges surrounding it. By convention, the singleton graph and 2-path graph are considered edge-transitive (B. McKay, pers. comm., Mar.
Is every simple connected 3 graph Vertex Transitive?
No. For example, the Frucht graph is 3 regular but not vertex transitive.
Which algorithm is used to find the transitive closure of the graph?
the Floyd Warshall Algorithm
A modified version of the Floyd Warshall Algorithm is used to find the Transitive Closure of the graph in O(V^3) time complexity and O(V^2) space complexity. to find the shortest distances between every pair of vertices in a given weighted edge Graph.
How do you prove edge transitivity?
In the mathematical field of graph theory, an edge-transitive graph is a graph G such that, given any two edges e1 and e2 of G, there is an automorphism of G that maps e1 to e2. In other words, a graph is edge-transitive if its automorphism group acts transitively on its edges.
Does a 3 regular graph on 14 vertices exist?
If k 1 = 4 and k 2 = 4 , then is isomorphic to and hence, by Theorem 1.1, there is a 3-regular, 3-connected subgraph of on 14 vertices.
How many 3 graphs does 6 vertices have?
All the six vertices have constant degree equal to 3. The edges of the graph are indexed from 1 to nd 2 = 6×3 2 = 9.
Is Petersen graph 1 Factorable?
Petersen graph can be partitioned into a 1-factor (red) and a 2-factor (blue). However, the graph is not 1-factorable.
Can a vertex transitive graph be a symmetric graph?
Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular. However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze’s graph).
Is the truncated tetrahedron a vertex transitive graph?
However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron ), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze’s graph ). The edges of the truncated tetrahedron form a vertex-transitive graph (also a Cayley graph) which is not symmetric.
When is a vertex transitive graph called quasi isometric?
Two countable vertex-transitive graphs are called quasi-isometric if the ratio of their distance functions is bounded from below and from above. A well known conjecture stated that every infinite vertex-transitive graph is quasi-isometric to a Cayley graph.
When is the vertex connectivity equal to the degree d?
The edge-connectivity of a vertex-transitive graph is equal to the degree d, while the vertex-connectivity will be at least 2 ( d + 1)/3. If the degree is 4 or less, or the graph is also edge-transitive, or the graph is a minimal Cayley graph, then the vertex-connectivity will also be equal to d.