Constructions Of H-Antimagic Graphs Using Smaller Edge-Antimagic Graphs.
Dafik Dafik, Slamin Slamin, Dushyant Tanna, Andrea Semaničová–Feňovčíková, Martin Bača · NOVA (University of Newcastle Australia) · 2017
A simple graph G = (V, E) admits an H-Covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H. An (a, d)-H-antimagic labeling of G admitting an H-covering is a bijective function f : V ∪ E → {1, 2, ..., ∣V∣ + ∣E∣} such that, for all subgraphs H' of G isomorphic to H, the H'-weights, etf(H') = Συ∈V(H')f(υ)+Σe∈E(H')F(e), constitute an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if f(V) = {1, 2, ..., ∣V∣}. In this paper, we study the existence of super (a, d)-H-antimagic labelings for graph operation GH, where G is a (super) (b, d*)-edge-antimagic total graph and H is a connected graph of order at least 3.