jariazavalverde / graphs

A generator of graphs written in Python and LaTeX

Generator of graphs

This repository contains tools and resources for generating, drawing and exporting diverse families of graphs in several formats (DIMACS, LaTeX, etc).

Usage

./graphs.py name parameters [options]

Options:

• -o path | -output path: exports the graph to a file. Default: standard output.
• -f name | -format name: selects the format of the graph: c, dimacs, haskell, javascript, prolog, python, numpy. Default: numpy.

Families

• Complete graphs
• Friendship graphs
• Generalized Petersen graphs
• Johnson graphs
• Windmill graphs

Complete graphs

A complete graph is an undirected graph in which every pair of distinct vertices is connected by a unique edge.

./graphs.py complete n

where:

• n > 0

K(10)	K(11)	K(12)

The file complete.tex defines a LaTeX command \complete{n} for drawing any complete graph with TikZ.

Friendship graphs

A friendship graph F(n) is a planar undirected graph with 2n+1 vertices and 3n edges, constructed by joining n copies of the cycle graph C(3) with a common vertex.

./graphs.py friendship n

where:

• n > 0

F(3)	F(4)	F(5)

The file friendship.tex defines a LaTeX command \friendship{n} for drawing any friendship graph (for n > 1) with TikZ.

Generalized Petersen graphs

The generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph.

./graphs.py petersen n k

where:

• n > 0
• k > 0
• k < n/2

GP(5, 1)	GP(5, 2)	GP(7, 1)

The file petersen.tex defines a LaTeX command \petersen{n}{k} for drawing any generalized Petersen graph with TikZ.

Johnson graphs

Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J(n, k) are the k-element subsets of an n-element set, where two vertices are adjacent when the intersection of the two vertices (subsets) contains (k-1)-elements.

./graphs.py johnson n k

where:

• n > 0
• k > 0
• k < n

J(4, 1)	J(4, 2)

Windmill graphs

The windmill graph Wd(k,n) is an undirected graph constructed for k > 1 and n > 1 by joining n copies of the complete graph K(k) at a shared universal vertex.

./graphs.py windmill k n

where:

• k > 1
• n > 1

Wd(4, 6)	Wd(9, 5)

The file windmill.tex defines a LaTeX command \windmill{k}{n} for drawing any windmill graph with TikZ.