Table 2 Notation adopted for modeling chemical compounds
Symbol | Designation |
|---|---|
\(\Lambda \) | A set of labels representing chemical elements |
\(\text {mass}({\mathtt{a}})\) | Atomic mass of chemical element \({\mathtt{a}}\in \Lambda \) |
\({\text {val}}({\mathtt{a}})\) | Valence of chemical element \({\mathtt{a}}\in \Lambda \) |
\(\text {mass}^*({\mathtt{a}})\) | \(\lfloor 10\cdot \text {mass}({\mathtt{a}})\rfloor \), \({\mathtt{a}}\in \Lambda \) |
\({\mathtt{a}}< \mathtt{b}\) | A total order over labels in the set \(\Lambda \), indicating \(\text {mass}({\mathtt{a}}) < \text {mass}(\mathtt{b})\) |
\(\gamma = ({\mathtt{a}}, \mathtt{b}, m)\) | Adjacency configuration for an atom pair, \({\mathtt{a}}, \mathtt{b}\in \Lambda \), \(m \in [1, 3]\) |
\(\overline{\gamma }\) | For an adjacency configuration \(\gamma = ({\mathtt{a}}, \mathtt{b}, m)\), \(\overline{\gamma } = (\mathtt{b}, {\mathtt{a}}, m)\) |
\(\Gamma _<\) | Set of adjacency configurations \(\gamma = ({\mathtt{a}}, \mathtt{b}, m) \in \Lambda \times \Lambda \times [1, 3]\) with \({\mathtt{a}}< \mathtt{b}\) |
\(\Gamma _>\) | Set of adjacency configurations \(\Gamma _> = \{ \overline{\gamma } \mid \gamma \in \Gamma _< \}\) |
\(\Gamma _=\) | Set of adjacency configurations, \(\Gamma _= = \{ ({\mathtt{a}}, {\mathtt{a}}, m) \mid {\mathtt{a}}\in \Lambda , m = [1, 3] \}\) |
\(\Gamma \) | \(\Gamma = \Gamma _< \cup \Gamma _=\) |
\(\alpha \) | A mapping of atom labels in \(\Lambda \) to graph vertices |
\(\beta \) | A mapping of integers in [1, 3] to graph edges, overloaded as \(\beta (u) = \sum _{uv \in E(H)} \beta (uv)\) for vertices \(u \in V(H)\) in a graph H |
\(\text {Bc}\) | Set of bond-configurations \(\mu \in [1, 4] \times [1, 4] \times [1, 3]\) |