Properties
The Coxeter graph has chromatic number 3, chromatic index 3, radius 4, diameter 4 and girth 7. It is also a 3-vertex-connected graph and a 3-edge-connected graph.
The Coxeter graph is hypohamiltonian : it does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from it is Hamiltonian. It has rectilinear crossing number 11, and is the smallest cubic graph with that crossing number currently known, but an 11-crossing, 26-vertex graph may exist (sequence A110507 in OEIS).
The Coxeter graph may be constructed from the smaller distance-regular Heawood graph by constructing a vertex for each 6-cycle in the Heawood graph and an edge for each disjoint pair of 6-cycles.
Read more about this topic: Coxeter Graph
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (18031882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (16321704)