There is no (95,40,12,20) strongly regular graph

Abstract

We show that there is no $(95,40,12,20)$ strongly regular graph and, consequently, there is no $(96,45,24,18)$ strongly regular graph, no two-graph on $96$ vertices, and no partial geometry $\mathrm{pg}(5,9,3)$. The main idea of the result is based on the star complement technique and requires a small amount of computation.

14 pages. arXiv admin note: substantial text overlap with arXiv:1509.05933