ALL GRAPHS ON A NON-PRIME NUMBER OF VERTICES ARE DESTRUCTIBLE
Wayne Goddard, Paul August Winter · Quaestiones Mathematicae · 1985
A connected, nontrivial, simple graph of order v is said to be α,β destructible if α,β are integral factors of v and an α-set of edges, E', exists whose removal from G isolates exactly the vertices in a β-set V'. Graphs which are not α, β destructible for any α.β are called stable. In this paper we prove that all graphs on a non-prime number v of vertices are α,β destructible for some a which divides v.