How do you draw a Petersen graph?
How do you draw a Petersen graph?
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges….
| Petersen graph | |
|---|---|
| The Petersen graph is most commonly drawn as a pentagon with a pentagram inside, with five spokes. | |
| Named after | Julius Petersen |
| Vertices | 10 |
| Edges | 15 |
What is the size of Petersen graph?
The Petersen graph is maximally non-Hamiltonian: there is a Hamiltonian path between any two nonadjacent vertices. There are 12 pentagons, 10 hexagons, 0 heptagons, 15 octagons 20 nonagons and 0 decagons. The binary code spanned by the cycles is a [15,6,5]-code.
How many faces are in a Petersen graph?
The Petersen graph can be embedded in the real projective plane with 6 faces (as the quotient of a dodecahedron by the antipodal map), or on the torus with 5 faces.
Is Petersen graph self centered?
For n\ge 3, the generalized Petersen graph P(n, 1) is a d-self-centered graph, where d = \lfloor \frac{n}{2} \rfloor + 1. Vertex transitive graphs are self-centered.
How do you find a bipartite graph?
The steps of this algorithm are:
- Assign a red color to the starting vertex.
- Find the neighbors of the starting vertex and assign a blue color.
- Find the neighbor’s neighbor and assign a red color.
- Continue this process until all the vertices in the graph are assigned a color.
How many cycles does the Petersen graph have?
Petersen Graph
| property | value |
|---|---|
| Hamiltonian graph | no |
| Hamiltonian cycle count | 0 |
| Hamiltonian path count | 240 |
| hypohamiltonian graph | yes |
What is the connectivity of Petersen graph?
The r-component connectivity of G denoted as κr(G) is the minimum cardinality of an r- component cut. That is, κr(G) is the minimum number of vertices that must be removed from G in order to obtain a graph with at least r connected components. Therefore, κ2(G) = κ(G), the connectivity of G.
