A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the otherâ€¦ (More)

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of theâ€¦ (More)

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of theâ€¦ (More)

For a simple connected undirected graph G,Ï‡(G), Ï‡ f (G), f (G), Ï†(G), âˆ‚ (G) and (G) denote respectively the chromatic number, fall chromatic number (assuming that it exists for G), fall achromaticâ€¦ (More)

Let G be a finite connected simple graph and Î¼(G) be the Mycielskian of G. We show that for connected graphs G and H, Î¼(G) is isomorphic to Î¼(H) if and only if G is isomorphic to H. Furthermore, weâ€¦ (More)