PELABELAN GRACEFUL PADA BEBERAPA JOIN GRAPH

Abstrak

Let G := ( V,E ) be a graph  with a non-empty vertex set   V and an edge set  E . The graph G is called ( p,q ) graph if | V ( G )| = p and | E ( G )| = q . Graceful labeling on graph  G is injective mapping  f : V ( G ) ? {0 , 1 , 2 ,...,q} such that it satisfies the induced mapping f ^{, which is defined by} f ⁽ uv ) = | f ( u )? f ( v )| for each edge uv in G , is a bijection from E ( G ) to {1 , 2 , 3 ,...,q }. A graph G that has a graceful label is called  a graceful graph . Let G and  H be two unconnected graphs. Join from G andH , which is denoted by G + H , is the graph obtained by connecting every vertex in  G and every vertex in  H . If G and H are ( m,s ) graph and ( n,t ) graph , respectively, then the join of the two graphs will have mn + s + t edges. In this paper, we will study graceful labeling on two types of join graphs , namely:  P ( m,s ) + I ( n,t) and P ( m, s ) + P ( n, t ).