Chromatic Number of Transformation Graphs of a Path

Abstract

A proper vertex coloring of a graph G is a bijection c:V(G)→{1,2,3,...,k} such that c(u) ≠c(v)
whenever uv ∈E(G). The minimum k for which G admits a proper coloring is called the
chromatic number of Gand is denoted by χ(G). A coloring c of Gwith span χ(G) is called an
optimal coloring of G. In this paper, we determine chromatic number of all the transformation
graph of apath