Bilangan Kromatik Graceful Pada Keluarga Graf Grid

Abstract

All graph in this paper be a connected and simple graph. Let c:V(G)→{1,2,…,k} is a proper vertex coloring where k ≥ 2 which induces a proper edge coloring c':E(G)→{1,2,…,k} define by c' (uv)=|c(u)-c(v)|, where uv in E(G) is called graceful k-coloring. A vertex coloring c of graph G is a graceful coloring if c is a graceful k-coloring for some k∈ N. The minimum k for which a graph G is a graceful chromatic number denoted by χ_g (G). In this paper, we will investigate the establish exact value of graceful chromatic number on grid graph family namely H graph 〖(H〗_n) for n≥2 and grid graph for m,n≥3.

Keywords: graceful coloring, graceful chromatic number, grid graph family