On super (a, d)-edge-antimagic total labeling of Möbius ladder

Abstract

A Möbius ladder is a simple graph obtained by introducing a twist in a prism graph. A Möbius ladder which has n pairs vertices is denoted by Mn. A graph G is called (a, d)-edge-antimagic total if there exists a bijection f from V (G) ∪ E (G) to {1, 2, …, |V (G) + E (G)|} such that the edge-weights, wf (uv) = f (u) + f (uv) + f (v), uv ∈ E (G), forms an arithmetic sequence with the first term a and common difference d. Further, it called super if f (V) = {1, 2, …, |V (G)|}. In this paper we proved that Mn is super (a, d)-edge-antimagic total with 0 ≤ d ≤ 2. Further, we showed that for every even n, Mn is not (a, 0)-edge-antimagic total.