Paper Info
Title
On triple systems and strongly regular graphs
Abstract
The block graph of a Steiner triple system of order v is a (v(v-1)/6,3(v-3)/2,(v+3)/2,9) strongly regular graph. For large v, every strongly regular graph with these parameters is the block graph of a Steiner triple system, but exceptions exist for small orders. An explanation for some of the exceptional graphs is here provided via the concept of switching. (Group divisible designs corresponding to) Latin squares are also treated in an analogous way. Many new strongly regular graphs are obtained by switching and by constructing graphs with prescribed automorphisms. In particular, new strongly regular graphs with the following parameters that do not come from Steiner triple systems or Latin squares are found: (49,18,7,6), (57,24,11,9), (64,21,8,6), (70,27,12,9), (81,24,9,6), and (100,27,10,6).
Year
DOI
Venue
2012
10.1016/j.jcta.2012.03.013
J. Comb. Theory, Ser. A
Keywords
DocType
Volume
steiner triple system,large v,prescribed automorphisms,following parameter,regular graph,block graph,group divisible,order v,exceptional graph,latin square,switching,strongly regular graph
Journal
119
Issue
ISSN
Citations 
7
0097-3165
4
PageRank 
References 
Authors
0.51
6
3
Name
Order
Citations
PageRank
Majid Behbahani171.37
Clement Lam2599.25
Patric R. J. Östergård360970.61