The $\text{SCR}$ representation of a graph $G=(V,E)$ is $C_{G}$ id the following conditions hold:
- $C_{G}$ is a combinatorial circuit with memory.
- $C_{G}$ has two inputs of length $n$ bits.
- $C_{G}$ has $r$ gates, where $r = \mathcal{O}(n^{k})$ for some integer $k$. link
- The output of $C_{G}$ is $$C_{G}(i',j') = 0, \text{if } (v_i,v_j) \in E$$ $$C_{G}(i',j') = 1, \text{if } (v_i,v_j) \notin E$$ $$C_{G}(i',j') = ?, \text{if } (v_i \in V) \text{ or } (v_j \notin V) $$
The binary representation of $i$ is $i'$. For certain graphs there is a representation in $\text{SCR}$ that takes logarithmic space in $|V|$.
Question : What are the graph classes(bounded degree, planar etc) which takes logarithmic space representation in $\text{SCR}$ model?
