Super Antimagicness of a Well-defined Graph

Abstract

A graph G of order p and size q is called an (a, d)-edge- antimagic total if there exist a bijection f : V (G)U E(G) ---> {1,2,3,4,5,...., 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 connected and disconnected of a well-defined mountain graph and also show a new concept of a permutation of an arithmetic sequence.