On super antimagicness of generalized flower and disk brake graphs

Abstract

Let G be a simple graph of order |V | and size |E|. An (a, d)- edge-Antimagic total labeling of G is a one-to-one mapping f taking the vertices and edges onto {1, 2, . . . , |V | + |E|} such that the edgeweights w(uv) = f(u)+f(v)+f(uv), uv ∈ E(G) form an arithmetic sequence {a, a + d, . . . , a + (|E| - 1)d}, where the first term a > 0 and the common difference d ≥ 0. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we will study a super antimagicness of generalized flower and disk brake graphs.