Differences between revisions 41 and 43 (spanning 2 versions)
 ⇤ ← Revision 41 as of 2007-06-17 21:13:00 → Size: 2284 Editor: D-69-91-137-177 Comment: ← Revision 43 as of 2007-06-19 08:31:53 → ⇥ Size: 2342 Editor: c-67-183-18-7 Comment: Deletions are marked like this. Additions are marked like this. Line 16: Line 16: == NEW ==Vertex colors for 3d graphsattachment:dod.png Line 24: Line 26: * (done) graph isomorphism and automorphism, graph6 and sparse6 formatting, database of small graphs, eigenvalues and eigenspaces, characteristic and minimal polynomials, cayley graphs * (done) graph isomorphism and automorphism, graph6 and sparse6 formatting, database of small graphs, eigenvalues and eigenspaces, characteristic and minimal polynomials, cayley graphs, edge colorings Line 26: Line 28: * (easy) edge colorings, bipartite graphs, point graph, line graph, graph from set and binary function, vertices as vector subspaces, generating trees * (easy) bipartite graphs, point graph, line graph, graph from set and binary function, vertices as vector subspaces, generating trees

# Graph Theory

[:days4/projects/: Other SAGE Days 4 Project]

Participants: Emily Kirkman, Robert Miller, Craig Citro and David Roe

# Cayley Graph of \$A_5\$
sage: G = sage.groups.perm_gps.permgroup.AlternatingGroup(5)
sage: C = G.cayley_graph()
sage: C.show3d(vertex_size=0.01, arc_size=0.005, arc_size2=0.008, xres=1000, yres=800)

## BEFORE

attachment:before.png

## AFTER

attachment:after.png

## NEW

Vertex colors for 3d graphs attachment:dod.png

• (done) Latex Graphs: Craig Citro & Robert Miller -- write an eps file to be included in LaTeX documents.

• (done) NetworkX 1: Expose these in SAGE: centrality, cliques, cluster, cores, search.
• [http://sage.math.washington.edu/home/rlmill/wshlst.pdf Wishlist] from Chris Godsil. Most feasible first.

• (done) graph isomorphism and automorphism, graph6 and sparse6 formatting, database of small graphs, eigenvalues and eigenspaces, characteristic and minimal polynomials, cayley graphs, edge colorings
• (easy) bipartite graphs, point graph, line graph, graph from set and binary function, vertices as vector subspaces, generating trees
• (medium) certain types of curves for plotting edges, generator based on geng
• (tedium) databases: ted spence, gordon royle
• (hard) max indep. set, chromatic number, hamilton cycles and paths, chromatic polynomial, tutte polynomial, cut vertices, vertex/edge connectivity, planarity
• Graph Database: Update interface to sqlite database of all graphs with 8 or fewer vertices.
• Emily Kirkman is currently working on this.
• Electrical Networks, Jim Morrow's REU: Graphs with boundary are already in sage, but there are probably some useful constructions for Jim's summer REU that are not implemented yet. Especially data structures, perhaps an ElectricalNetworks class. Look at the Dirichlet problem, graphs on surfaces and (circular) planar embeddings of graphs.

• Bipartite Class
• NetworkX 2:
• spectrum -- This should probably not be wrapped, but instead mimicked, since sage's linear algebra is undoubtedly faster.
• hybrid, threshold -- Figure out what these are?

days4/projects/graphs (last edited 2008-11-14 13:41:54 by localhost)