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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 graph encoded in either Sparse6 or Graph6 format
• G, ,
• 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 graph isomorphic to $S$ encoded in either Sparse6 or Graph6 format
• H, , 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.

• relabelBipartite -- relabels a bipartite graph so all vertices of a given class are contiguous

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 .