Subdivided trees are integral sum graphs (Q2477401)

A graph \(G\) is an integral sum (IS) graph if there exists a labeling of its vertices with distinct integers such that for every pair of distinct vertices \(u,v\in V(G)\), \(uv\in E(G)\) if and only if \(u+v\in V(G)\). IS graphs were introduced by \textit{F. Harary} [Discrete Math. 124, 99--105 (1994; Zbl 0797.05069)]. The main result of the paper is that every subdivided tree (each edge is subdivided by at least one vertex) is an IS graph.