Some extremal families of edge-regular graphs

Regular clique assemblies, configurations, and friendship in Edge-Regular graphs

“…In [8] the edge-regular graphs with λ = 2 and n = 3(d − λ) are completely characterized, and in [12] the main result in [8] is extended to a characterization of all edge-regular graphs satisfying n = 3(d −λ) with λ > 0 even and d sufficiently large (depending on λ).…”

“…. , P k+1 and on the graphs H j ∈ E R (12,4,1) obtained by inserting edges among the vertices of P j , j = 1, . .…”

“…For any choice of the P j , and any insertion of the edges of one of the graphs in E R (12,4,1) on the vertices of the P j , j = 1, . .…”