cocktailParty -- Returns a cocktail party graph

Synopsis

Usage:

G = cocktailParty n
Inputs:
- n, an integer, The number of vertices on each side; there will be 2*n total vertices
Outputs:
- G, a graph, The cocktail party graph

Description

The cocktail party graph with respect to an integer n is a graph with 2*n vertices. Its edge set is formed by taking a disjoint union of n path graphs on 2 vertices and taking its complement, yielding an edge set of every possible edge except for those that were initially adjacent on the ladder.

i1 : cocktailParty 4

o1 = Graph{0 => {1, 2, 3, 5, 6, 7}}
           1 => {0, 2, 3, 4, 6, 7}
           2 => {0, 1, 3, 4, 5, 7}
           3 => {0, 1, 2, 4, 5, 6}
           4 => {1, 2, 3, 5, 6, 7}
           5 => {0, 2, 3, 4, 6, 7}
           6 => {0, 1, 3, 4, 5, 7}
           7 => {0, 1, 2, 4, 5, 6}

o1 : Graph

Ways to use cocktailParty :

cocktailParty(ZZ)

For the programmer

The object cocktailParty is a method function.