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:

$i = 0$: 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 : G = graph {{0,1},{1,2},{2,3},{3,4},{0,4}}

o1 = Graph{0 => {1, 4}}
           1 => {0, 2}
           2 => {1, 3}
           3 => {2, 4}
           4 => {0, 3}

o1 : Graph

i2 : relabelGraph G

o2 = Graph{0 => {1, 2}}
           1 => {0, 3}
           2 => {0, 4}
           3 => {1, 4}
           4 => {2, 3}

o2 : 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