{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T04:09:41Z","timestamp":1725509381634},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>With the aid of computer algebra systems COCO and GAP with<\/jats:p><jats:p>its packages we are investigating all seven known primitive<\/jats:p><jats:p>triangle-free strongly regular graphs on 5, 10, 16, 50, 56,<\/jats:p><jats:p>77 and 100 vertices. These graphs are rank 3 graphs, having<\/jats:p><jats:p>a rich automorphism group. The embeddings of each graph<\/jats:p><jats:p>from this family to other ones are described, the<\/jats:p><jats:p>automorphic equitable partitions are classified, all<\/jats:p><jats:p>equitable partitions in the graphs on up to 50 vertices are<\/jats:p><jats:p>enumerated. Basing on the reported computer aided results<\/jats:p><jats:p>and using techniques of coherent configurations, a few new<\/jats:p><jats:p>models of these graphs are suggested, which are relying on<\/jats:p><jats:p>knowledge of just a small part of symmetries of a graph in<\/jats:p><jats:p>consideration.<\/jats:p>","DOI":"10.29007\/bdgp","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T22:59:06Z","timestamp":1516748346000},"page":"108-91","source":"Crossref","is-referenced-by-count":0,"title":["Computer algebra investigation of known primitive triangle-free strongly regular graphs"],"prefix":"10.29007","volume":"15","author":[{"given":"Matan","family":"Ziv-Av","sequence":"first","affiliation":[]},{"given":"Mikhail","family":"Klin","sequence":"additional","affiliation":[]}],"member":"11545","event":{"name":"SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T22:59:08Z","timestamp":1516748348000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/BbN2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/bdgp","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}