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On h-antimagicness of disconnected graphs

Abstract:

A simple graph G = (V; E) admits an H-covering if every edge in E belongs to at least one subgraph of G isomorphic to a given graph H. Then the graph G is (a; d)-H-antimagic if there exists a bijection f : ∪ E → {1, 2, V + E} such that, for all subgraphs H0 of G isomorphic to H, the H-weights, wtf (H) =∑vv(H') f(v)+∑e∈(H') f(e) form an arithmetic progression with the initial term a and the common difference d. When f (V) = {1; 2 V}, then G is said to be super (a; d)-H-antimagic. In this paper, we study super (a, d)-H-antimagic labellings of a disjoint union of graphs for d = E(H) -V(H).