Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph

Abstract

Let G be a simple graph of order p and size q. Graph G is called an (a,d)-edge-antimagic total if there exist a bijection f : V (G) ∪ E(G) → {1, 2,...,p + q} such that the edge-weights, w(uv) = f(u)+f(v)+f(uv); u, v ∈ V (G), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a,d)-edge antimagic total properties of connected of Ferris Wheel FWm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs 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 feasible d.