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

Abstract

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.