On graphs whose local subgraphs are strongly regular with parameters \((144, 39, 6, 12)\)
A graph \(\Gamma\) is called an edge-regular graph with parameters \((v, k, \lambda)\) if it is a regular graph of degree \(k\) on \(v\) vertices and each of its edges lies in \(\lambda\) triangles, and it is called an amply regular graph with parameters \((v, k, \lambda, \mu)\) if it is an edge-regular graph with the corresponding parameters and any two vertices \(a,b\) of \(\Gamma\) such that their distance \(d(a,b)=2\) have exactly \(\mu\) common neighbors. As a consequence of two theorems in this paper concerning amply regular graphs whose local subgraphs are strongly regular graphs with parameters \((144,39,6,12)\), the following corollary is deduced: Let \(\Gamma\) be an amply regular graph whose local subgraphs are strongly regular graphs with parameters \((144, 39, 6, 12)\). Then the following assertions hold: (1) \(\Gamma\) is not a distance-regular graph; (2) \(\Gamma\) is not a locally \(\Delta\)-graph, where \(\Delta\) is a known strongly regular graph with parameters \((144, 39, 6, 12)\) and automorphism group \(\mathrm{SL}_{3}(3)\).
scientific article; zbMATH DE number 6355658