ON STABLE GRAPHS

Abstract

A connected, nontrivial, simple graph G 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. Classes of stable graphs are provided and critically stable graphs of prime order are characterized.