Global Parameters

Let  be a simple connected graph, and take , where  is the graph diameter. Then  has global parameters  (respectively , ) if the number of vertices at distance  (respectively, , ) from a given vertex  that are adjacent to a vertex  at distance  from  is the constant  (respectively , ) depending only on  (i.e., not on  of ).

Global parameters may be computed by the GRAPE package in GAP using the function GlobalParameters(G), which returns a list of length  whose th element is the list  (except that if some global parameter does not exist then  is put in its place). Note that  is a distance-regular graph iff this function returns no  in place of a global parameter.

A distance-regular graph with global parameters  has intersection array .