63.33 LocalParameters

LocalParameters( gamma, V )
LocalParameters( gamma, V, G )

This function determines any local parameters c_i(<V>), a_i(<V>), or b_i(<V>) that simple, connected gamma may have, with respect to the singleton vertex or vertex set V (see BCN89). The function returns a list of triples, whose i-th element is [c_{i-1}(<V>),a_{i-1}(<V>),b_{i-1}(<V>)], except that if some local parameter does not exist then a -1 is put in its place. This function can be used to determine whether a given subset of the vertices of a graph is a distance-regular code in that graph.

The optional parameter G, if present, is assumed to be a subgroup of Aut(<gamma>) fixing V (setwise). Including such a G can speed up the function.

    gap> LocalParameters( JohnsonGraph(4,2), 1 );
    [ [ 0, 0, 4 ], [ 1, 2, 1 ], [ 4, 0, 0 ] ]
    gap> LocalParameters( JohnsonGraph(4,2), [1,6] );
    [ [ 0, 0, 4 ], [ 2, 2, 0 ] ] 

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