Element neighbourhoods in twofold triple systems
A twofold triple system TTS(v) is a (v,3,2)-design. The neighbourhood N(p) of the point p is the multigraph on \(V\setminus \{p\}\) (V the point set) with an edge \(\{\) x,y\(\}\) for every block \(\{\) p,x,y\(\}\) through p. Thus N(p) is a 2-regular multigraph on v-1 vertices. The authors prove that every 2-regular multigraph on \(n\equiv 0\) or 2 (mod 3) vertices occurs as a neighbourhood graph in a TTS, with two exceptions (vis. \(C_ 2\cup C_ 3\) and \(C_ 3\cup C_ 3)\). The proof uses difference methods.
scientific article; zbMATH DE number 4012623
scientific article