is the path joining the distinct leaves $\{x_1\}$ and $\{x_2\}$ in $T_X$, then we have $$d(x_1, x_2) = \max_{v \in V(P)} l(v),$$ where the labeling $l \colon V(T_X) \to \mathbb{R}^{+}$ is defined as in .

The next section of the paper contains several results which can be considered as extensions of Theorem \[t2.9\] to the case of unrooted, labeled trees.

Comments on the concept of graph isomorphism {#comments-on-the-concept-of-graph-isomorphism .unnumbered}
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All above introduced notions of tree isomorphism can be considered as some specifications of the following general definition.

Let $G = (V, E, L_V, L_E, l)$ be a graph with $V(G) = V$, $E(G) = E$ and such that $L_V$ and $L_E$ are some sets of vertex labels and edge labels, respectively, and let $f \colon (V \cup E) \to L_V \cup L_E$ be a mapping for which $f(V) \subseteq L_V$ and $f(E) \subseteq L_{E}$ hold.

\[d2.11\] The graphs $$G_1 = (V_1, E_1, L_{V_1}, L_{E_1}, l_1) \quad \text{and} \quad G_2 = (V_2, E_2, L_{V_2}, L_{E_2}, l_2)$$ are isomorphic if there is a bijection $f \colon V_1 \to V_2$ such that:

1.  \[d2.11:s1\] $l_1(v) = l_2(f(v))$ for every $v \in V_1$.

2.  \[d2.11:s2\] $(\{u, v\} \in E_1) \Leftrightarrow (\{f(u), f(v)\} \in 