Tree-Antimagicness of Disconnected Graphs

Abstract EN

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.