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… Click to show full abstract
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.
               
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