| dc.description.abstract | Let G be a simple, connected and undirected graph. Given r; k as any natural numbers. By an
r-dynamic k-coloring of graph G, we mean a proper k-coloring c(v) of G such that jc(N(v))j
minfr; d(v)g for each vertex v in V (G), where N(v) is the neighborhood of v. The r-dynamic
chromatic number, written as
(G), is the minimum k such that G has an r-dynamic k-coloring.
We note that the 1-dynamic chromatic number of graph is equal to its chromatic number, denoted
by (G), and the 2-dynamic chromatic number of graph has been studied under the name
a dynamic chromatic number, denoted by
r
(G). By simple observation, we can show that
r
(G)
r+1
(G), however
r+1
(G)
r
d
(G) can be arbitrarily large, for example (Petersen) =
2;
d
(Petersen) = 3, but
3
(Petersen) = 10. Thus, finding an exact values of
(G) is not trivially
easy. This paper will describe some exact values of
(G) when G is an operation of special
graphs. | en_US |
