Super (a, d)-edge antimagic total labelings of friendship and generalized friendship graphs

An (a, d)-edge-antimagic total labeling of a graph G with p vertices and q edges is a bijection f from the set of all vertices and edges to the set of positive integers {1,2,3,…,p+q} such that all the edge-weights w(uv)=f(u)+f(v)+f(uv); uv∈E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called a super (a, d)-edge-antimagic total labeling ((a, d)-SEAMT labeling) if f(V(G))={1,2,3,…,p}. In this paper we investigate the existence of super (a, d)-edge antimagic total labeling for friendship graphs and generalized friendship graphs.