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| Graceful Coloring of Wheel Graph Family |
Siti Khoirunnisa, Dafik, Arika Indah Kristiana, Ridho Alfarisi
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Abstract:
All graph in this paper are connected and simple graph. A proper vertex coloring f:V(G)?{1, 2, ..., k}, where k=2 which induces a proper edge coloring f:E(G)?{1, 2, ..., k-1} define by f'(uv)=|f(u)-f(v)| is called a graceful k -coloring. If f is a graceful k-coloring for some k?N, then a vertex coloring f of graph G is a graceful coloring. Graceful chromatic number of G, denoted by ?_g (G), is the minimum k for which G has a graceful k-coloring. In this paper, we determine the exact value of the graceful chromatic number of some wheel graph family, namely gear graph, helm graph, closed helm graph, flower graph, and web graph.
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