Super Antimagicness of Triangular Book and Diamond Ladder Graphs

Abstract

A graph G of order p and size q is called an (a, d)-edge-antimagic total if there exists a bijection f : V (G) U E(G) ---> {1, 2, .... , p + q} such that the edge-weights, w(uv) = f(u)+f(v)+f(uv); uv in 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 Triangular Book and Diamond Ladder graphs. The result shows that there are a super (a, d)-edge-antimagic total labeling of graph Bt_n and Dl_n, if n > 1 with d in {0, 1, 2}