Emily Kirkman is working on this project.

The goal of the Graph Generators Class is to implement constructors for many common graphs, as well as thorough docstrings that can be used for reference. The graph generators will grow as the Graph Theory Project does. So please check back for additions and feel free to leave requests in the suggestions section.

We currently have 30 constructors of named graphs and basic structures. Most of these graphs are constructed with a preset dictionary of x-y coordinates of each node. This is advantageous for both style and time. (The default graph plotting in SAGE using the spring-layout algorithm). SAGE graphs all have an associated graphics object, and examples of plotting options are shown on the graphs below.

As we implement algorithms into the Graph Theory Package, the constructors of known graphs would set their properties upon instantiation as well. For example, if someone created a very large complete bipartite graph and then asked if it is a bipartite graph (not currently implemented), then instead of running through an algorithm to check it, we could return a value set at instantiation. Further, this will improve the reference use of the docstrings as we would list the properties of each named graph.

Due to the volume of graphs now in the generators class, this wiki page is now intended to give status updates and serve as a gallery of graphs currently implemented. To see information on a specific graph, run SAGE or the SAGE [http://sage.math.washington.edu:8100 notebook]. For a list of graph constructos, type "graphs." and hit tab. For docstrings, type the graph name and one question mark (i.e.: "graphs.CubeGraph?") then shift + enter. For source code, do likewise with two question marks.

The SAGE [http://sage.math.washington.edu:9001/graph Graph Theory Project] aims to implement Graph objects and algorithms in ["SAGE"].

TableOfContents

Suggestions

• ???

Graphs I Plan to Add

Inherited from NetworkX

• Bipartite Generators
• Balanced tree
• Dorogovstev golstev mendes graph
• Grid (n-dim)
• Chvatal
• Desargues
• Pappus
• Sedgewick
• Truncated cube
• Truncated tetrahedron
• Tutte
• Also many more random generators and gens from degree sequence to sort through

Families of Graphs

• Generalized Petersen graphs
• Petersen Graph family
• Trees (Directed – not simple. Maybe Balanced tree constructor and query isTree)
• Cayley (Requires Edge Coloring)
• Paley

Named Graphs

• Brinkman
• Clebsch
• Icosahedron
• Grötzsch graph
• Tutte eight-cage
• Szekeres snark
• Thomassen graph
• Johnson (maybe own class)
• Turan

Gallery of Graph Generators in SAGE

Named Graphs

Flower Snark

sage: flower_snark = graphs.FlowerSnark()
sage: flower_snark.set_boundary([15,16,17,18,19])
sage: flower_snark.show(figsize=[4,4], graph_border=True)

Frucht

Heawood

Moebius Kantor

Petersen

Thomsen

Graph Families

Complete Bipartite Graphs

Complete Graphs

Cube Graphs

Basic Structures

Barbell Graph

Bull Graph

Circular Ladder Graph

Claw Graph

Cycle Graphs

Diamond Graph

Dodecahedral Graph

Empty Graph

Grid 2d Graph

House Graph

House X Graph

Krackhardt Kite Graph

Ladder Graph

Lollipop Graph

Octahedral Graph

Path Graph

Star Graph

Tetrahedral Graph

Wheel Graph

Random Generators

Random GNP

Random GNP Fast