Here - Combinatorial algorithms and algorithmic graph theory

8 Introduction
Figure 1.2: A parent graph with isomorphic children.
called pseudosimilarity of construction operations.
Isomorphic graphs can also be obtained from different parents. For example
when the basic edge insertion operation is applied to the dashed pairs of edges
of the non-isomorphic graphs G and G ′ of Figure 1.4, they yield two isomorphic
graphs: H and H ′ , respectively.
The canonical construction path method takes care of all of these sources of
isomorphism. When using this method, we first have to define, for every graph
G of the class of graphs which we want to generate, a canonical reduction which
is unique up to isomorphism. We call the graph which is obtained by applying
the canonical reduction to G the canonical parent of G and an expansion that is
the inverse of a canonical reduction a canonical expansion. The two rules of the
canonical construction path method are:
1. Only accept a graph if it was constructed by a canonical expansion.
2. For every graph G to which construction operations are applied, only perform
one expansion from each equivalence class of expansions of G.
Note that accepting a graph if it was constructed from a canonical parent
would not be sufficient, as this does not eliminate pseudosimilarity. A canonical
graph is a graph which was constructed by a canonical expansion.
The canonical construction path method is applied in most of the generation
algorithms which are described in this thesis. More specifically, it is used for