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Let \( G \) be a graph with vertex set \( V(G) \) and edge set \( E(G) \). For a labeling \( f: V(G) \to A = \{0, 1\} \), define a partial edge labeling \( f^*: E(G) \to A \) such that, for each edge \( xy \in E(G) \),
\[
f^*(xy) = f(x) \quad \text{if and only if} \quad f(x) = f(y).
\]
For \( i \in A \), let
\[
\text{v}_f(i) = |\{ v \in V(G) : f(v) = i \}|
\]
and
\[
\text{e}_{f^*}(i) = |\{ e \in E(G) : f^*(e) = i \}|.
\]
A labeling \( f \) of a graph \( G \) is said to be friendly if
\[
|\text{v}_f(0) – \text{v}_f(1)| \leq 1.
\]
If a friendly labeling \( f \) induces a partial labeling \( f^* \) such that
\[
|\text{e}_{f^*}(0) – \text{e}_{f^*}(1)| \leq 1,
\]
then \( G \) is said to be balanced. In this paper, a necessary and sufficient condition for balanced graphs is established. Using this result, the balancedness of several families of graphs is also proven.