Antimagicness of star forests

Abstract

An edge labeling of a graph G is a bijection : E(G)-> {1,2, • • ▪, £(G)}. The induced vertex sum + of is a function defined on V{G) given by +(u) = £uwfi(C)(,) for all u V(G). The value f+(u) is called the vertex sum at u. The graph G is called antimagic if there exists an edge labeling of G such that the vertex sums at all vertices of G Eire distinct. A star forest is the union of disjoint stars. Let Sn denote a star with n edges, and mSn denote a star forest consisting of the disjoint m copies of Sn. It is known that mS2 is antimagic if find only if m = 1. In this study, a necessary condition and a sufficient condition sire obtained whereby a star forest mS2 U Sm U S,2 U • • • U Snk (m, ri2, • • •, nfc > 3) may be antimagic. In addition, a necessary and sufficient condition is obtained whereby a star forest rnSa U S, (n > 3) may be antimagic. Moreover, a graph consisting of disjoint stars together with an extra disjoint path is also verified to be antimagic. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.