Content deleted Content added
→Basic relationship between parameters: clarify per talk |
|||
Line 101:
# 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>
===Adjacency matrix equations===
| |||