Decomposition dimension

Decomposition dimension --- декомпозитная размерность.

A decomposition ${\mathcal F} = \{F_{1}, \ldots, F_{r}\}$ of the edge set of a graph $G$ is called a resolving $r$-decomposition, if for any pair of edes $e_{1}$ and $e_{2}$ there exists an index $i$ such that $d(e_{1},F_{i}) \neq d(e_{2},F_{i})$, where $d(e,F)$ denotes the distance from $e$ to $F$. The decomposition dimension $dec(G)$ of a graph $G$ is the least integer $r$ such that there exists a resolving $r$-decomposition.

See also

• Metric dimension.