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...

Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph, the Heawood graph and the vertices and edges of the Platonic...

vertex-transitive. Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need...

v ≤ w. The transitive closure of a DAG is the graph with the most edges that has the same reachability relation as the DAG. It has an edge u → v for every...

graph is a graph that is edge-transitive but not vertex-transitive. A half-transitive graph is a graph that is vertex-transitive and edge-transitive but...

The edge chromatic number of a graph G is equal to the vertex chromatic number of its line graph L(G). The line graph of an edge-transitive graph is vertex-transitive...

Petersen graph is strongly regular (with signature srg(10,3,0,1)). It is also symmetric, meaning that it is edge transitive and vertex transitive. More strongly...

  For the transitive closure of a directed graph, see transitive. 2.  A closure of a directed graph is a set of vertices that have no outgoing edges to vertices...

mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible,...

Bruijn graph Dense graph Dipole graph Directed acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive graph Interval...

and each edge contributes the same amount (one) to both numbers. Every regular bipartite graph is also biregular. Every edge-transitive graph (disallowing...

vertex-transitive, arc-transitive, and distance-transitive graphs; strongly regular graphs and their generalizations distance-regular graphs. Two edges of...

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...

the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after Girard...

Arc-transitive graph, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices Edge-transitive graph, a graph whose...

families of graphs based on symmetry (such as symmetric graphs, vertex-transitive graphs, edge-transitive graphs, distance-transitive graphs, distance-regular...

connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the...

{\displaystyle G} . The Cayley graph Γ = Γ ( G , S ) {\displaystyle \Gamma =\Gamma (G,S)} is an edge-colored directed graph constructed as follows: Each...

mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and...

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...

is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices...

specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs...

take any edge to any other edge, making the Higman–Sims graph an edge-transitive graph. The outer elements induce odd permutations on the graph. As mentioned...

In graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive...

McColl, W. F.; Noshita, K. (1986), "On the number of edges in the transitive closure of a graph", Discrete Applied Mathematics, 15 (1): 67–73, doi:10...

In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph. A...

graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs...

graph is simple) connected in a closed chain. The cycle graph with n vertices is called Cn. The number of vertices in Cn equals the number of edges,...

Triangular prism graph – 6 vertices, 9 edges Cubical graph – 8 vertices, 12 edges Pentagonal prism graph – 10 vertices, 15 edges Hexagonal prism graph – 12 vertices...

star with 3 edges is called a claw. The star Sk is edge-graceful when k is even and not when k is odd. It is an edge-transitive matchstick graph, and has...