SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH

Abstract. An (a, d)-edge-antimagic total labeling of G is a one-to-one mapping taking the vertices and edges onto {1, 2, 3, . . . , p + q} Such that the edge-weights w(uv) = (u)+(v)+(uv), uv ∈ E(G) form an arithmetic sequence {a, a+d, a+2d, . . . , a+ (q − 1)d}, where first term a > 0 and common difference d ≥ 0. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we will study a super edge-antimagic total labelings properties of connective Swn graph. 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. Key Words: (a, d)-edge-antimagic total labeling, super (a, d)-edge-antimagic total labeling, Silkworm graph