SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH - Hadi, Dian Anita; Dafik, D; Slamin, S (KadikmA, 2015)
Abstract. An Â (a, d)-edge-antimagic Â totalÂ Â labeling Â of G Â is a Â one-to-one Â mapping taking the vertices and edges onto 1, 2, 3, . . . , p + q Such that the edge-weights w(uv) Â = (u)+(v)+(uv), uv â E(G) Â form an arithmetic sequence a, a+d, a+2d, . . . , a+ (q â 1)d, where first term Â a > 0 and Â common Â difference d â¥ 0. Â Such a graph G is called super if the smallest possible labels appear on the vertices. Â In this paper we will study a super edge-antimagic total labelings properties of connective Swn graph.Â Â The result shows that a connected Silkworm graph admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all the feasible n, d. Â Key Words: (a, d)-edge-antimagic total labeling, super (a, d)-edge-antimagic total labeling, Silkworm graph.