Canonical Labelling

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The graph canonical labelling problem is to find a function
canon : GVGV, s.t.
canon(G) is isomorphic to G, and
canon(Gγ) = canon(G),   ∀γ∈Sn,
where the Vertex set V = {1, ..., n}, Sn is the [group] of all permutations over V, GV is the set of all graphs over V, and G∈GV.
Note, graphs G and G' are isomorphic iff canon(G) = canon(G').
One approach is to seek a labelling of G that gives the largest possible adjacency matrix, read as a binary number in some order, for example,
136 ...
248 ...
579 ...
... ... ... ...
If self-loops are not allowed, the diagonal can be ignored.
If the graph is undirected, only the right-upper (or left-lower) triangle need be considered.

(It may be convenient to make V = {0, ..., n-1} in programs.)




Search for [canonical labelling maths graph] in the [bib].


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