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Tree-antimagicness of disconnected graphs

Abstract:

A simple graph G admits an H -covering if every edge in E (G) belongs to a subgraph of G isomorphic to H. The graph G is said to be (a, d)- H -antimagic if there exists a bijection from the vertex set V (G) and the edge set E (G) onto the set of integers 1, 2,., V G + E (G) such that, for all subgraphs H ′ of G isomorphic to H, the sum of labels of all vertices and edges belonging to H ′ constitute the arithmetic progression with the initial term a and the common difference d. G is said to be a super (a, d)- H -antimagic if the smallest possible labels appear on the vertices. In this paper, we study super tree-antimagic total labelings of disjoint union of graphs.