Partial Difference Triples
Ka Hin Leung
and Siu Lun Ma
DOI: 10.1023/A:1022475918250
Abstract
It is known that a strongly regular semi-Cayley graph (with respect to a group G) corresponds to a triple of subsets ( C, D, D | G | \textonesuperior 8 |G| \ne 8 nor 25, all partial difference triples come from a certain family of partial difference triples. Second, we investigate partial difference triples over cyclic group. We find a few nontrivial examples of strongly regular semi-Cayley graphs when | G| is even. This gives a negative answer to a problem raised by de Resmini and Jungnickel. Furthermore, we determine all possible parameters when G is cyclic. Last, as an application of the theory of partial difference triples, we prove some results concerned with strongly regular Cayley graphs.
Pages: 397–409
Keywords: strongly regular graph; semi-Cayley graph; partial difference triple; difference set
Full Text: PDF
References
1. K.T. Arasu and Q. Xiang, "On the existence of periodic complementary binary sequences,"