Dear GAP-Forum,

Hi all,
I suppose some of you must have tried gap for generating or
testing some graph theoretic properties, such as perfect matching,
edge colouring, etc.

May I have some examples of such applications?

Thank you all.

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Javaid Aslam    Architecture Validation Tools
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The GRAPE share library package in GAP deals mostly with graph problems
related to group theory and finite geometry. For example, recent additions
to GRAPE include an algorithm to classify the partial linear spaces
with given point graph and parameters, and an algorithm to determine
all distance-regular generalized orbital graphs for a given transitive
permutation group.

That said, there are still some useful GRAPE functions for people
doing research in other fields. In particular, the GRAPE function
CompleteSubgraphsOfGivenSize is a powerful tool for classifying complete
subgraphs of a given size. The latest version can also be used to
classify complete subgraphs with a given vertex-weight sum in a graph
with vertices with positive integer weights.

A good way of seeing many GRAPE functions is to type

??graph

at the GAP prompt (you will also see some stuff about other
things, like chrystallographic groups). Better still, look at
the Chapter GRAPE in the HTML GAP Manual.

Best wishes, Leonard Soicher.

P.S. Not all the new features and algorithms are documented yet,
although the comments with the code explain how to use them.
If more people want to use the new features then this will provide
me with motivation to update the manual section!