The neighbourhood of an element in a triple system of index λ is the λ-regular multigraph whose edges are the unordered pairs appearing in triples with the fixed element. We prove, for every λ, that every λ-regular simple graph meeting the necessary congruence and density conditions appears as the neighbourhood of an element. Applications in design theory are given.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics