Global Parameters
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
www.almerja.com
الجزء والصفحة:
...
23-4-2022
2425
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 ![[c_(i-1),a_(i-1),b_(i-1)]](https://mathworld.wolfram.com/images/equations/GlobalParameters/Inline23.svg)
(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 ![[[c_0,a_0,b_0],[c_1,a_1,b_1],[c_2,a_2,b_2],[c_3,a_3,b_3],[c_4,a_4,b_4]]](https://mathworld.wolfram.com/images/equations/GlobalParameters/Inline27.svg)
has intersection array ![<span style=]()
{b_0,b_1,b_2,b_3;c_1,c_2,c_3,c_4}" src="https://mathworld.wolfram.com/images/equations/GlobalParameters/Inline28.svg" style="height:24px; width:224px" />.
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