On r-Dynamic Coloring of Some Special Graphs Operations
Ika Hesti Agustin, Dafik Dafik, N.I. Wulandari · 2017
Let G be a simple, connected and undirected graph. Let r; k be natural number. By a proper k -coloring of a graph G , we mean a map c : V ( G ) ! S , where jSj = k , such that any two adjacent vertices receive di®erent colors. An r -dynamic k -coloring is a proper k -coloring c 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 and c ( S ) = fc ( v ) : v 2 Sg for a vertex subset S . The r -dynamic chromatic number, written as  r ( G ), is the minimum k such that G has an r -dynamic k -coloring. The 1-dynamic chro-matic 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  d ( G ). By simple observation it is easy to see that  r ( G ) ·  r +1 ( G ), for example  ( C 6 ) = 2, but  d ( C 6 ) = 3. In this paper we will show the exact values of some graph operation of special graphs.