Abstract
Graph isomorphism (GI) has occupied both theoreticians
and applied scientists since the early 1950s. Over the years, several
approaches and algorithms with which an isomorphism between two
graphs can be tested have been developed. A general approach is the
Weisfeiler–Lehman (WL) test, which is based on a coloring algorithm
and provides a necessary criterion for graph isomorphism. However, the
WL test is restricted to examining graphs with only node attributes.
Therefore, this paper presents two extensions of the WL algorithm to
allow for testing on arbitrary graphs. One considers edge attributes, and
the other tests the isomorphism on dynamic graphs. Additionally, we
extend the WL-hierarchy by the attributed and dynamic WL tests and
show that it is a partial order, which induces a lattice. In the future, this
may allow for practical implications coming from lattice theory.
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