Super Total Labeling (a,d)- edge Antimagic on the Firecracker Graph

Abstract

An (a, d)-edge-antimagic total labeling on (p, q)-graph G is a one-to-one map f from V (G) ∪ E(G) onto the  integers 1, 2, . . . , p + q with the property that the edge-weights, w(uv) = f (u)+ f (v) + f (uv) where uv ∈  E(G),form an arithmetic progression starting from a and having common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge antimagic total labeling of Firecracker Graph.