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Two constructions of H-antimagic graphs

Abstract:

Let H be a graph. A graph G=(V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. A graph G admitting an H-covering is called (a,d)-H-antimagic if there is a bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that for each subgraph H′ of G isomorphic to H, the sum of labels of all the edges and vertices belonged to H′ constitute the arithmetic progression with the initial term a and the common difference d. Such a graph is called super if f(V(G))={1,2,3,…,|V(G)|}. In this paper, we provide two constructions of (super) H-antimagic graphs obtained from smaller (super) H′-antimagic graphs.