Every bipartite graph is an induced subgraph of a sum graph

A finite simple graph G is called an integral sum graph(respectively, sum graph)
if there is a bijection f from the vertices of G to a set of integers S (respectively, a
set of positive integers S) such that uv is an edge of G if and only if f(u)+f(v) ∈ S.
In 1999, Liaw et al (Ars Comb.,Vol.54, 259-268) posed the conjecture that every
tree is an integral sum graph. In this note, we prove that every bipartite graph is
an induced subgraph of a sum graph G with sum number σ(G) = 1.