In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of...

mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two...

regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such...

Every distance-transitive graph is distance-regular. Indeed, distance-regular graphs were introduced as a combinatorial generalization of distance-transitive...

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...

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

the same distance apart. A semi-symmetric graph is a graph that is edge-transitive but not vertex-transitive. A half-transitive graph is a graph that is...

It is a distance-transitive graph (see the Foster census) and therefore distance regular. There are 24 perfect matchings in the Heawood graph; for each...

group of the graph. Despite its high degree of symmetry, the Petersen graph is not a Cayley graph. It is the smallest vertex-transitive graph that is not...

In the mathematical field of graph theory, the Livingstone graph is a distance-transitive graph with 266 vertices and 1463 edges. Its intersection array...

In 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...

graph is transitively closed if it equals its own transitive closure; see transitive. 4.  A graph property is closed under some operation on graphs if...

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

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

810 edges. It is a strongly regular graph, a distance-transitive graph, and a Ramanujan graph. Although its construction is folklore, it was named after...

which is not a distance-transitive graph. The n × n square rook's graph, i.e., the line graph of a balanced complete bipartite graph Kn,n, is an srg(n2, 2n − 2...

are known. The Foster graph is one of the 13 such graphs. It is the unique distance-transitive graph with intersection array {3,2,2,2,2,1,1,1;1,1,1,1,2...

a point. Vertex-transitive graph Generating set of a group Lovász conjecture Cube-connected cycles Algebraic graph theory Cycle graph (algebra) Proof:...

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...

shortest path distances in the Johnson graph. The Johnson scheme is also related to another family of distance-transitive graphs, the odd graphs, whose vertices...

Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability...

Grötzsch graph shares several properties with the Clebsch graph, a distance-transitive graph with 16 vertices and 40 edges: both the Grötzsch graph and the...

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...

graph with intersection array (6, 5, 2; 1, 1, 3). The Perkel graph is also distance-transitive. It is also the skeleton of an abstract regular polytope,...

vertex-transitive. H(2,3), which is the generalized quadrangle G Q (2,1) H(1,q), which is the complete graph Kq H(2,q), which is the lattice graph Lq,q...

Cayley graph, its automorphism group acts transitively on its vertices, making it vertex transitive. In fact, it is arc transitive, hence edge transitive and...

edge-graceful when k is even and not when k is odd. It is an edge-transitive matchstick graph, and has diameter 2 (when l > 1), girth ∞ (it has no cycles)...

the hypercubes that double cover them the property of being a distance-transitive graph. When k is odd, the dimension-k folded cube contains as a subgraph...

vertex. Walk-regular graphs can be thought of as a spectral graph theory analogue of vertex-transitive graphs. While a walk-regular graph is not neccessarily...

easily from the inductive construction.) is arc transitive and symmetric. The symmetries of hypercube graphs can be represented as signed permutations. contains...