Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Switching of edges in strongly regular graphs | Switching of edges in strongly regular graphs. I. A family of partial difference sets on 100 vertices L. K. J0rgensen Dept. of Math. Sciences Aalborg University Fr. Bajers Vej 7 9220 Aalborg Denmark leif@ M. Klin Department of Mathematics Ben-Gurion University 653 Beer-Sheva 84105 Israel. klin@ Submitted Aug 30 2002 Accepted Mar 29 2003 Published May 3 2003 MR Subject Classifications 05E30 Abstract We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters 100 22 0 6 100 36 14 12 100 45 20 20 100 44 18 20 . The existence of strongly regular graphs with the latter set of parameters was an open question. Our method is based on combination of Galois correspondence between permutation groups and association schemes classical Seidel s switching of edges and essential use of computer algebra packages. As a by-product a few new amorphic association schemes with 3 classes on 100 points are discovered. 1 Introduction Strongly regular graphs were frequently investigated during the last few decades in different contexts including group theory algebraic graph theory design of experiments finite geometries error-correcting codes etc. see Bro96 for a short digest of some important results in this area . The in a sense most symmetric strongly regular graphs are rank 3 graphs that is such graphs r that the automorphism group Aut r acts transitively on the vertices ordered pairs of adjacent vertices and ordered pairs of non-adjacent vertices. Rank 3 graphs play a significant role in group theory cf. Asc94 . The class of Cayley graphs forms a natural class of graphs with quite high symmetry the automorphism group of a Cayley graph Partially supported by Department of Mathematical Sciences University of Delaware Newark DE 19716 THE ELECTRONIC JOURNAL OF .
