VERTEX MAGIC TOTAL LABELING ON SUN DIGRAPHS

Listiana, Yuni and Darmaji, D and Slamin, S (2014) VERTEX MAGIC TOTAL LABELING ON SUN DIGRAPHS. In: MATHEMATICS EDUCATION AND GRAPH THEORY, 09 Juni 2014, Islamic University of Malang. (In Press)

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Abstract

Digraph D(V,A) is a graph which each of edge has orientation called arc. Notice that a set of vertices and a set of arcs on D respectively is denoted by V(D) and A(D), with s=|V(D)| and t=|A(D)|. A one-to-one map = V U A ==> (1,2,3,...,s+t) is a vertex magic total labeling if there is a constant k such that at any vertex y require to: ∑ (xy) + (y) - ∑ (yz) = k where A ⃗⃗⃗⃗(y) is a set of arcs that entering vertex y and A (y) is a set of arcs that leaving vertex y. In this paper, we describe how to construct vertex magic total labeling on suns digraph. Sun digraph,s defined as cycle digraph by adding an orientation pendant at each vertex of the cycle. The orientation of arcs in the sun digraph follow clockwise direction.

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