Abstract: For a positive integer r, a rhued coloring of a graph G is a mapping c: VG→1,2,…, k, such that：(1) if u,v∈VGare adjacent vertices in G, then cu≠cv; (2) for any v∈ VG, cNv≥minNv,r.N(v) is the set of vertices which are adjacent to vertex v. The smallest integer k, which let G have a proper (k,r)coloring, is defined as rhued chromatic number χrG. In this paper, the differences between χrG-vand χrG (d(v)=2) which caused by 2vertex deletion is investigated.

Key words: r-hued coloring, r-hued chromatic number, 2-vertex