Results 1 
5 of
5
Switching of edges in strongly regular graphs. I. A family of partial difference sets on 100 vertices
 ELECTRON. J. COMBIN., 10(1):RESEARCH PAPER
, 2003
"... We present 15 new partial difference sets over 4 nonabelian 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), (100,45,20,2 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We present 15 new partial difference sets over 4 nonabelian 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 byproduct, a few new amorphic association schemes with 3 classes on 100 points are discovered.
Analytical enumeration of circulant graphs with primesquared number of vertices
 Lotharing. Combin
, 1996
"... A method for the analytical enumeration of circulant graphs with p 2 vertices, p a prime, is proposed and described in detail. It is based on the use of Srings and P'olya's enumeration technique. Two different approaches, "structural " and "multiplier", are developed and compare ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
A method for the analytical enumeration of circulant graphs with p 2 vertices, p a prime, is proposed and described in detail. It is based on the use of Srings and P'olya's enumeration technique. Two different approaches, "structural " and "multiplier", are developed and compared. As a result we get counting formulae and generating functions (by valency) for nonisomorphic p 2vertex directed and undirected circulant graphs as well as for some natural subclasses of them such as tournaments and selfcomplementary graphs. These are the first general enumerative results for circulant graphs for which the socalled ' Ad'am (singlemultiplier) isomorphism condition does not hold. Some numerical data and interrelations between formulae are also obtained. The first expository part of the paper may serve as a selfcontained introduction to the use of Schur rings for enumeration.
A computer approach to the enumeration of block designs which are invariant with respect to a prescribed permutation group
, 1997
"... ..."
Computer Algebra Investigation of Known Primitive TriangleFree Strongly Regular Graphs
"... With the aid of computer algebra systems COCO and GAP with its packages we are investigating all seven known primitive trianglefree strongly regular graphs on 5, 10, 16, 50, 56, 77 and 100 vertices. These graphs are rank 3 graphs, having a rich automorphism group. The embeddings of each graph from ..."
Abstract
 Add to MetaCart
With the aid of computer algebra systems COCO and GAP with its packages we are investigating all seven known primitive trianglefree strongly regular graphs on 5, 10, 16, 50, 56, 77 and 100 vertices. These graphs are rank 3 graphs, having a rich automorphism group. The embeddings of each graph from this family to other ones are described, the automorphic equitable partitions are classified, all equitable partitions in the graphs on up to 50 vertices are enumerated. Basing on the reported computer aided results and using techniques of coherent configurations, a few new models of these graphs are suggested, which are relying on knowledge of just a small part of symmetries of a graph in consideration. 1
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
Abstract
 Add to MetaCart
We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.