On an adjacency property of graphs
Geoffrey Exoo · Journal of Graph Theory · 1981
Abstract A graph G has property A(m, n, k) if for any sequence of m + n distinct points of G, there are at least k other points, each of which is adjacent to the first m points of the sequence but not adjacent to any of the latter n points. the minimum order among all graphs with property A(m, n, k) is denoted a(m, n, k). Bounds are given on the numbers a(m, n, k) and some exact results are indicated.