Properties
The vertex-connectivity of a symmetric graph is always equal to the degree d. In contrast, for vertex-transitive graphs in general, the vertex-connectivity is bounded below by 2(d+1)/3.
A t-transitive graph of degree 3 or more has girth at least 2(t–1). However, there are no finite t-transitive graphs of degree 3 or more for t ≥ 8. In the case of the degree being exactly 3 (cubic symmetric graphs), there are none for t ≥ 6.
Read more about this topic: Symmetric Graph
Famous quotes containing the word properties:
“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)
“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)