Non-existence of (76,30,8,14) strongly regular graph

We prove the non-existence of strongly regular graph with parameters (76,30,8,14). We use Euclidean representation of a strongly regular graph together with a new lower bound on the number of 4-cliques to derive strong structural properties of the graph, and then use these properties to show that th...

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Bibliographic Details
Published in:	Linear algebra and its applications Vol. 527; pp. 53 - 72
Main Authors:	Bondarenko, A.V., Prymak, A., Radchenko, D.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 15-08-2017 American Elsevier Company, Inc
Subjects:	Euclidean representation Euclidean space Graph representations Graphical representations Graphs Linear algebra Lower bounds Mathematical models Number of cliques Strongly regular graph secondary Strongly regular graph Euclidean representation Number of cliques primary
Online Access:	Get full text
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Summary:	We prove the non-existence of strongly regular graph with parameters (76,30,8,14). We use Euclidean representation of a strongly regular graph together with a new lower bound on the number of 4-cliques to derive strong structural properties of the graph, and then use these properties to show that the graph cannot exist.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2017.03.033