Editing Strongly regular graph (section)

===Basic relationship between parameters===
The four parameters in an srg(''v'', ''k'', λ, μ) are not independent: In order for an srg(''v'', ''k'', λ, μ) to exist, the parameters must obey the following relation:
:<math>(v - k - 1)\mu = k(k - \lambda - 1)</math>

The above relation is derived through a counting argument as follows:
# Imagine the vertices of the graph to lie in three levels. Pick any vertex as the root, in Level 0. Then its ''k'' neighbors lie in Level 1, and all other vertices lie in Level 2.
# Vertices in Level 1 are directly connected to the root, hence they must have λ other neighbors in common with the root, and these common neighbors must also be in Level 1. Since each vertex has degree ''k'', there are <math>k - \lambda - 1</math> edges remaining for each Level 1 node to connect to vertices in Level 2. Therefore, there are <math>k (k - \lambda - 1)</math> edges between Level 1 and Level 2.
# Vertices in Level 2 are not directly connected to the root, hence they must have μ common neighbors with the root, and these common neighbors must all be in Level 1. There are <math>(v - k - 1)</math> vertices in Level 2, and each is connected to μ vertices in Level 1. Therefore the number of edges between Level 1 and Level 2 is <math>(v - k - 1)\mu</math>.
# Equating the two expressions for the edges between Level 1 and Level 2, the relation follows.

This relation is a [[necessary condition]] for the existence of a strongly regular graph, but not a [[sufficient condition]]. For instance, the quadruple (21,10,4,5) obeys this relation, but there does not exist a strongly regular graph with these parameters.<ref>{{citation
 | last1 = Brouwer | first1 = A. E.
 | last2 = van Lint | first2 = J. H.
 | contribution = Strongly regular graphs and partial geometries
 | contribution-url = https://pure.tue.nl/ws/portalfiles/portal/2394798/595248.pdf
 | isbn = 0-12-379120-0
 | mr = 782310
 | pages = 85–122
 | publisher = Academic Press, Toronto, ON
 | title = Enumeration and design (Waterloo, Ont., 1982)
 | year = 1984}}</ref>