Tree-Antimagicness of Disconnected Graphs

摘要

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, ..., vertical bar V(G)vertical bar+vertical bar E(G)vertical bar} 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.