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have no edges with only one node (loops; not a Comment: Graph theory is a rich source for
pseudograph). Derived from G. Rozenberg (per- pattern recognition algorithms.
sonal communication).
Grassman algebra See exterior algebra.
graph grammar A grammar over a set G of
graphs G(V, E). ground In logic and logic programming, a
Comment: Like a natural language or string term which is not, or does not include, a variable.
grammar, a graph grammar provides rules to Comment: The restriction is meant to avoid
generate, recognize, and transform graphs; for wiring confusion.
example, expanding a token for a substituent
group into the atoms and bonds of that group,
group (1) A defined linked collection of
or contracting the group to an abbreviation. Mir-
atoms or a single atom within a molecular entity.
roring the chemistry, one could form bonds and
The use of the term in physical organic and gen-
specify orientation by examining an atom’s con-
eral chemistry is less restrictive than the defini-
text. This suggests the grammar is context-
tion adopted for the purpose of nomenclature of
sensitive. However, to date the only formal
organic compounds.
proofs for molecular languages are that linear
(2) A set G with a binary operation which is
polymers such as DNA are greater than context-
associative. Each element is assumed to have an
free (noncontext-free), a superset which includes
inverse and G contains an identity element.
the context-sensitive grammars among its mem-
bers. So while it is reasonable to conjecture that
group homomorphism A map φ : G → H
molecules form a context-sensitive language,
between two groups such that
there is no formal proof yet.
φ(e ) = e H φ(g · g ) = φ(g ) · φ(g )
2
G
2
1
1
graph theory The branch of mathematics
dealing with the topological relationships among where e and e denote the identity elements of
G H
abstract graphs. the groups G and H, respectively.

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