Chromatic Edge Stability Number of a Graph

Let G be a graph with chromatic number (G) = k. The chromatic edge stability number es (G) is the minimum number of edges whose removal results in a graph G1 with (G1) = (G) 1. The chromatic bondage number (G) is the minimum number of edges between two color classes in a k coloring of G, where the minimum is taken over all k-colorings of G. We present several interesting results and unsolved problems on Chromatic edge stability number and Chromatic bondage number.