Editing Strongly regular graph (section)

===Geodetic graphs===
Every strongly regular graph with <math>\mu = 1</math> is a [[geodetic graph]], a graph in which every two vertices have a unique [[Shortest path problem|unweighted shortest path]].<ref name=bb>{{citation
 | last1 = Blokhuis | first1 = A.
 | last2 = Brouwer | first2 = A. E. | authorlink = Andries Brouwer
 | doi = 10.1007/BF00191941
 | issue = 1–3
 | journal = [[Geometriae Dedicata]]
 | mr = 925851
 | pages = 527–533
 | title = Geodetic graphs of diameter two
 | volume = 25
 | year = 1988
| s2cid = 189890651
 }}</ref> The only known strongly regular graphs with <math>\mu = 1</math> are those where <math>\lambda</math> is 0, therefore triangle-free as well. These are called the Moore graphs and are [[#The Hoffman–Singleton theorem|explored below in more detail]]. Other combinations of parameters such as (400, 21, 2, 1) have not yet been ruled out. Despite ongoing research on the properties that a strongly regular graph with <math>\mu=1</math> would have,<ref>{{citation
 | last1 = Deutsch | first1 = J.
 | last2 = Fisher | first2 = P. H.
 | doi = 10.1006/eujc.2000.0472
 | issue = 3
 | journal = [[European Journal of Combinatorics]]
 | mr = 1822718
 | pages = 303–306
 | title = On strongly regular graphs with <math>\mu=1</math>
 | volume = 22
 | year = 2001| doi-access = free
}}</ref><ref>{{citation
 | last1 = Belousov | first1 = I. N.
 | last2 = Makhnev | first2 = A. A.
 | issue = 2
 | journal = [[Doklady Akademii Nauk]]
 | mr = 2455371
 | pages = 151–155
 | title = On strongly regular graphs with <math>\mu=1</math> and their automorphisms
 | volume = 410
 | year = 2006
}}</ref> it is not known whether any more exist or even whether their number is finite.<ref name=bb/> Only the elementary result is known, that <math>\lambda</math> cannot be 1 for such a graph.