A graph G = (V, E) is said to be topogenic if it admits a topogenic set indexer, which is a set indexer f: Viƒ 2X such that f(V) f (E) iƒ… is a topology on X. A list colouring of a graph G = (V,E) with a colour list C = i» i€¨ i€© i€¨ i€© i½ 1 2 , , .... ( ) n c v c v c v for V = {v1, v2, ….vn} is a proper colouring of V by element of ( )j j c v so that the adjacent vertices u,v are coloured differently and the colour for viƒŽV is in C(V). L- edge colouring of a graph G is an assignment L:E(G)iƒ 2X-ia such that no two adjacent edges receive the same label where X is a ground set. A graph G is to be L- edge colourable if there exists an L- edge colouring of G. A comparative study of topogenic graphs and L- edge colourable graphs has been made in this paper.