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The problem of counting the number of independent sets of a graph G (denoted as i(G)) is a classic #P-complete problem. We present some patterns on graphs that allows us the polynomial computation of i(G). For example, we show that for a graph G where its set of cycles can be arranged as embedded cycles, i(G) can be computed in polynomial time. Particularly, our proposal counts independent sets on outerplanar graphs.

Basic Pattern Graphs for the Efficient Computation of Its Number of Independent Sets