A graph \(G(V,E)\) is called \((a,d)\)-edge antimagic total if there exists a bijection \(f: V(G) \cup E(G) \to \{1,2, \dots,|V(G)|+|E(G)|\}\) such that the edge-weights \(\Lambda(uv) = f(u) + f(uv) + f(v)\), \(uv \in E(G)\) form an arithmetic progression with first term \(a\) and common difference \(d\). It is called super \((a,d)\)-edge antimagic total if furthermore \(f(V(G)) = \{1,2,\dots,|V(G)|\}\). The main result obtained in this paper is the following. If a graph \(G(V,E)\) is super \((a,0)\)-edge antimagic total, then it is super \((a-|E(G)|+1,2)\)-edge antimagic total. Then the authors study the super \((a,d)\)-edge antimagic total labeling of fan graphs, bi-star graphs and extended bi-star graphs.