Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices at distance i - 1 (respectively, i, i + 1) from a given vertex v that are adjacent to a vertex w at distance i from v is the constant c_i (respectively a_i, b_i) depending only on i (i.e., not on v of w). Global parameters may be computed by the GRAPE package in GAP using the function GlobalParameters(G), which returns a list of length d(G) + 1 whose ith element is the list [c_(i - 1), a_(i - 1), b_(i - 1)] (except that if some global parameter does not exist then -1 is put in its place). Note that G is a distance-regular graph iff this function returns no -1 in place of a global parameter.

distance-regular graph | intersection array