  In this study, we address the independent set enumeration problem. Although
several efficient enumeration algorithms and careful analyses have been
proposed for maximal independent sets, no fine-grained analysis has been given
for the non-maximal variant. From the main result, we propose an algorithm
$\texttt{EIS}$ for the non-maximal variant that runs in $O(q)$ amortized time
and linear space, where $q$ is the clique number, i.e., the maximum size of a
clique in an input graph. Note that $\texttt{EIS}$ works correctly even if the
exact value of $q$ is unknown. Despite its simplicity, $\texttt{EIS}$ is
optimal for graphs with a bounded clique number, such as, triangle-free graphs,
planar graphs, bounded degenerate graphs, locally bounded expansion graphs, and
$F$-free graphs for any fixed graph $F$, where a $F$-free graph is a graph that
has no copy of $F$ as a subgraph.
