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 $$\mu \in [1, 4] \times [1, 4] \times [1, 3]$$ 