Constructions of strongly regular Cayley graphs using index four Gauss sums
نویسندگان
چکیده
We give a construction of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.
منابع مشابه
Strongly Regular Graphs from Union of Cyclotomic Classes
We give two constructions of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new parameters.
متن کاملConstructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes
In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions given by Feng and Xiang [10, 12]. Three infinite families of strongly regular graphs with new parameters are obtained. The main tools that we employed are i...
متن کاملCyclotomy, Gauss Sums, Difference Sets and Strongly Regular Cayley Graphs
We survey recent results on constructions of difference sets and strongly regular Cayley graphs by using union of cyclotomic classes of finite fields. Several open problems are raised.
متن کاملStrongly Regular Semi-Cayley Graphs
We consider strongly regular graphs r = (V, E) on an even number, say 2n, of vertices which admit an automorphism group G of order n which has two orbits on V. Such graphs will be called strongly regular semi-Cayley graphs. For instance, the Petersen graph, the Hoffman-Singleton graph, and the triangular graphs T(q) with q = 5 mod 8 provide examples which cannot be obtained as Cayley graphs. We...
متن کاملStrongly regular Cayley graphs over primary abelian groups of rank 2
Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [5] and [12]. It was shown that such graphs exist iff the corresponding group is isomorphic to Zpn ⊕Zpn , where p is an odd prime. In this paper we classify all strongly regular Cayley graphs over this group using Schur rings method. As a consequence we obtain a complete classification of strongly...
متن کامل