Antimagic labeling of linear forests

Abstract

A graph with q edges is called antimagic if its edges can be labeled with 1,2, ..., q such that the sums of the labels of the edges incident to each vertex are distinct. A linear forest is the union of disjoint paths of orders greater than one. A JVfree linear forest is a linear forest without any path P_k as its components. It is shown that P₂, P₃,A-free linear forests are antimagic. This study improves the result and shows that P₂, P₃-free linear forests are antimagic. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.