Some New Results on Proper Colouring of Edge-set Graphs

In this paper, we present a foundation study for proper colouring of edge-set graphs. The authors consider that a detailed study of the colouring of edge-set graphs corresponding to the family of paths is best suitable for such foundation study. The main result is deriving the chromatic number of the edge-set graph of a path, $P_{n+1}$, $n\ge 1$. It is also shown that edge-set graphs for paths are perfect graphs.