Computer algebra investigation of known primitive triangle-free strongly regular graphs

16 pages•Published: June 19, 2013

Abstract

With the aid of computer algebra systems COCO and GAP with
its packages we are investigating all seven known primitive
triangle-free 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.

Keyphrases: computer algebra, equitable partitions, strongly regular graphs

In: Laura Kovács and Temur Kutsia (editors). SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science, vol 15, pages 108--123

Links:	https://easychair.org/publications/paper/BbN2
	https://doi.org/10.29007/bdgp