NAME
Graph::Maker::Johnson  create Johnson graphs
SYNOPSIS
use Graph::Maker::Johnson;
$graph = Graph::Maker>new ('Johnson', N => 8, K => 3);
DESCRIPTION
Graph::Maker::Johnson
creates Graph.pm
graphs of Johnson graphs. Each vertex is a Kmany subset of the integers 1 to N. Edges are between vertices which have K1 integers the same and 1 integer different. Vertex names are the list of K integers separated by commas, such as "1,5,6,8".
An N,K graph is the same as an N,NK but different vertex names.
K=1 or K=N1 is the completeN graph. For K=1, the vertex names are the same as Graph::Maker::Complete
(integers 1 to N).
K=2 or K=N2 is the triangular graph, which is the line graph of the completeN graph.
N=5,K=2, which is triangular5, is the complement of the Petersen graph. The Petersen graph can be considered as the Kneser 5,2 which is edges between pairs of integers with both different, whereas here edges between one different. (Neither has edges for none different as that would be selfloops.)
FUNCTIONS
$graph = Graph::Maker>new('Johnson', key => value, ...)

The key/value parameters are
N => integer K => integer graph_maker => subr(key=>value) constructor, default Graph>new
Other parameters are passed to the constructor, either
graph_maker
orGraph>new()
.If the graph is directed (the default) then edges are added both forward and backward between vertices. Option
undirected => 1
creates an undirected graph and for it there is a single edge between vertices.
HOUSE OF GRAPHS
House of Graphs entries for the graphs here include
 N=4, K=2, https://hog.grinvin.org/ViewGraphInfo.action?id=226
 N=5, K=2, https://hog.grinvin.org/ViewGraphInfo.action?id=21154 (complement of Petersen)
SEE ALSO
Graph::Maker, Graph::Maker::Kneser, Graph::Maker::Petersen
LICENSE
Copyright 2015, 2016, 2017, 2018, 2019 Kevin Ryde
This file is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.
This file is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with This file. If not, see http://www.gnu.org/licenses/.