Abstract
A graph G(V, E) admits an (a, d)-H-antimagic covering if every edge in E(G) belongs to H′ subgraph of G that is isomorphic to H and there exists a bijective function f : V (G) ∪ E(G) → 1, 2,…, |V (G)| + |E(G)| such that for all subgraphs H′ isomorphic to H, the H′-weights, w(H′) = ∑vεV (H′) f (v) + ∑eεE(H′) f(e) constitutes an arithmetic progression a, a + d,…, a + (t − 1)d, where a and d are some positive integers and t is the number of subgraphs isomorphic to H. If the label of vertices are {1, 2, …, |V (G)|}, then it is called super (a, d)-H-antimagic covering. In this paper we find super (a, d)-H-antimagic covering on double star graph Sn,n, union of star graph mSn and union of double star graph mSn,n.
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