ON α,β DESTRUCTIBLE GRAPHS

Abstract

A connected simple graph G or 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'. Aspects of α,β destructions of graphs considered include associated reconstruction problems, unique α,β destructibility, annihilability and proper division sequences of numbers associated with paths.