Abstract
A graph G = ( V , E ) is an integral sum graph ( ISG) if there exists a labeling S ( G ) ⊂ Z such that V = S ( G ) and for every pair of distinct vertices u , v ∈ V , uv is an edge if and only if u + v ∈ V . A vertex in a graph is called a fork if its degree is not 2. In 1998, Chen proved that every tree whose forks are at distance at least 4 from each other is an ISG. In 2004, He et al. reduced the distance to 3. In this paper we reduce the distance further to 2, i.e. we prove that every tree whose forks are at least distance 2 apart is an ISG.
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