relabelGraph -- applies a vertex invariant based refinement to a graph

Synopsis

Usage:

L' = relabelGraph(L, i, a)

L' = relabelGraph(L, i)

L' = relabelGraph L

T = relabelGraph(S, i, a)

T = relabelGraph(S, i)

T = relabelGraph S

H = relabelGraph(G, i, a)

H = relabelGraph(G, i)

H = relabelGraph G
Inputs:
- L, a list, a list of graphs in various formats
- S, a string, a graph encoded in either Sparse6 or Graph6 format
- G, a graph,
- i, an integer, a choice of invariant to order by ($0 \leq i \leq 15$, default is $0$)
- a, an integer, a non-negative argument passed to nauty, (default is $3$)
Outputs:
- L', a list, a list of graphs isomorphic to $S$
- T, a string, a graph isomorphic to $S$ encoded in either Sparse6 or Graph6 format
- H, a graph, a graph isomorphic to $G$

Description

This method applies one of sixteen vertex invariant based refinements to a graph. See the nauty documentation for a more complete description of each and how the argument $a$ is used.

The sixteen vertex invariants are: \break \ \ \ \ $i = 0$: none,
\ \ \ \ $i = 1$: twopaths,
\ \ \ \ $i = 2$: adjtriang(K),
\ \ \ \ $i = 3$: triples,
\ \ \ \ $i = 4$: quadruples,
\ \ \ \ $i = 5$: celltrips,
\ \ \ \ $i = 6$: cellquads,
\ \ \ \ $i = 7$: cellquins,
\ \ \ \ $i = 8$: distances(K),
\ \ \ \ $i = 9$: indsets(K),
\ \ \ \ $i = 10$: cliques(K),
\ \ \ \ $i = 11$: cellcliq(K),
\ \ \ \ $i = 12$: cellind(K),
\ \ \ \ $i = 13$: adjacencies,
\ \ \ \ $i = 14$: cellfano, and
\ \ \ \ $i = 15$: cellfano2.

i1 : R = QQ[a..e];

i2 : G = graph {a*e, e*c, c*b, b*d, d*a};

i3 : relabelGraph G

o3 = Graph{"edges" => {{a, b}, {a, c}, {b, d}, {c, e}, {d, e}}}
           "ring" => R
           "vertices" => {a, b, c, d, e}

o3 : Graph

Note that on most small graphs, all sixteen orderings produce the same result.

Ways to use relabelGraph :

relabelGraph(Graph)
relabelGraph(Graph,ZZ)
relabelGraph(Graph,ZZ,ZZ)
relabelGraph(List)
relabelGraph(List,ZZ)
relabelGraph(List,ZZ,ZZ)
relabelGraph(String)
relabelGraph(String,ZZ)
relabelGraph(String,ZZ,ZZ)

For the programmer

The object relabelGraph is a method function.

relabelGraph -- applies a vertex invariant based refinement to a graph

Synopsis

Description

See also

Ways to use relabelGraph :

For the programmer