1,4

The symmetry means that any two vertices and any two edges are equivalent. In other words, if we have an initial labeling of the graph with vertices A and B adjacent (directly connected by an edge), we can relabel any two adjacent vertices as A and B, and then relabel the remaining vertices so that new graph will be equal to the initial.

Wolfram MathWorld Symmetric Graph.

The complete graph is symmetrical.

In addition, if the number of vertices is > 3, the simple cycle through all vertices is symmetrical.

Graphs determined by vertices and edges of Platonic solids are symmetrical.

The square K X K grid with right vertices connected to corresponding left vertices and bottom vertices connected to corresponding top vertices is symmetrical.

The smallest nontrivial and non-Platonic symmetric graph is the hexagon with connected opposite vertices.

An example of symmetrical graph with 13 vertices:

0 connected to 1, 2, 3, 4

1 connected to 0, 5, 6, 7

2 connected to 0, 5, 8, 9

3 connected to 0, 6, 10, 11

4 connected to 0, 8, 10, 12

5 connected to 1, 2, 10, 11

6 connected to 1, 3, 8, 12

7 connected to 1, 8, 9, 11

8 connected to 2, 4, 6, 7

9 connected to 2, 7, 10, 12

10 connected to 3, 4, 5, 9

11 connected to 3, 5, 7, 12

12 connected to 4, 6, 9, 11

Cf. A087145.

Adjacent sequences: A133178 A133179 A133180 this_sequence A133182 A133183 A133184

Sequence in context: A121895 A139555 A088371 this_sequence A090397 A054704 A143525

hard,nice,nonn

Eugene Vasilchenko (eugene(AT)vasilchenko.net), Oct 10 2007, Oct 14 2007