PELABELAN γ − PADA PATH DAN CYCLE

Priyanto, (2009) PELABELAN γ − PADA PATH DAN CYCLE. Other thesis, Universitas Sebelas Maret.

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Abstract

Priyanto, 2009. − γ LABELING of PATH AND CYCLE , Faculty of Mathematic and Natural Science, Sebelas Maret University. A graph explained set of points called vertices and together with lines called edge. A − γ labeling of a graph G of order |V(G)| and size |E(G)| is a one­to­one function, f : V(G) → { 0, 1, 2, ..., | E(G)| } that induces a labeling f’ : E(G) → { 1, 2, ..., |E(G)| } of the edges of G, f’(e) = | f (u) – f (v) for edge e = uv of G. Value of − γ labeling f denoted by val(f) = ∑ ∈ ) ( ) ( ' G E e e f . The maximum value of − γ labeling of G is defined by val max (G) = max{val(f) : f is a − γ labeling of G}. And the minimum value of − γ labeling of G is defined by val min (G) = min {val(f) : f is a − γ labeling of G}. The aims of research are to describe − γ labeling of path and cycle and resulting of the maximum and minimum values. The method on this research is a literary study. The result shows that 1. val min (P n ) = n – 1, val max (P n ) =       − 2 2 2 n for every integer n ≥ 2 2. val min (C n ) = 2(n ­ 1), val max (C n ) = 2 ) 3 )( 1 ( + − n n for every odd integer n ≥ 3 and val max (C n ) = 2 ) 2 ( + n n for every even integer n ≥ 4.

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