Super (a, d)-edge antimagic total labelings of friendship graphs.
S. Arumugam, M. Nalliah · NOVA (University of Newcastle Australia) · 2012
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.