γ - Uniquely colorable graphs
M. Yamuna, A. Elakkiya · IOP Conference Series Materials Science and Engineering · 2017
A graph G = ( V, E ) is uniquely colorable if the chromatic number χ ( G ) = n and every n – coloring of G induces the same partition of V. In this paper, we introduce a new kind of graph called γ - uniquely colorable graphs. We obtain a necessary and sufficient condition for a graph to be γ - uniquely colorable graphs. We provide a constructive characterization of γ - uniquely colorable trees.