generalizedPetersenGraph -- Returns a generalized petersen graph
Synopsis
Usage:
G = generalizedPetersenGraph (n, k)
Inputs:
n, an integer, The number of vertices will be 2*n, n in the outer ring and n in the inside ring
k, an integer, The middle ring is a complete graph but looks like a star, k is the number of vertices that get jumped for each connection k must be less than n/2.
Outputs:
G, an object of class Graph (missing documentation), The generalized petersen graph
Description
The generalized Petersen Graph is a class of graphs with a particular edge set. There are two equal sets of vertices and each set is a cycle graph. This forms two disjoint cyclegraphs. Then each inside edge connects to an adjacent outside edge, similar to the circular ladder graph. The outer loop keeps a more "canonical" order for the cycle, in the sense that it does not "skip" vertices, while the inner cycle takes on a "star-like pattern" that jumps vertices but is still connected.