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*the [[Games graph]] (729,112,1,20).{{r|br}}
Other potentially-valid combinations with <math>\lambda=1</math> include (99,14,1,2) and (115,18,1,3) but it is unknown whether strongly regular graphs with those parameters exist.{{r|mak}} The question of the existence of a strongly regular graph with parameters (99,14,1,2) is known as [[Conway's 99-graph problem]], and [[John Horton Conway]] has offered a $1000 prize for its solution.{{r|zd}}
There are finitely many [[distance-regular graph]]s of degree 4 or 6 that are locally linear. Beyond the strongly regular graphs of the same degrees, they also include the line graph of the Petersen graph, the Hamming graph <math>H(3,3)</math>, and the [[Bipartite half|halved]] [[Foster graph]].{{r|hns}}
==Density==
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| volume = 23
| year = 1996}}</ref>
<ref name=hns>{{citation
| last1 = Hiraki | first1 = Akira
| last2 = Nomura | first2 = Kazumasa
| last3 = Suzuki | first3 = Hiroshi
| doi = 10.1023/A:1008776031839
| issue = 2
| journal = Journal of Algebraic Combinatorics
| mr = 1761910
| pages = 101–134
| title = Distance-regular graphs of valency 6 and <math>a_1=1</math>
| volume = 11
| year = 2000}}</ref>
<ref name=lpv>{{citation
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