P2, -P3, P4-free linear forests are antimagic

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 a graph consisting of some disjoint paths of orders greater than one. And a P_k-free linear forest is a linear forest without any path P_k as its components. This paper shows that P₂,p₃,P₄-ixee linear forests are antimagic.