Abstract
We consider the number of vertex independent sets $i(G)$. In general, the problem of determining the value of $i(G)$ is $NP$-complete. We present several upper and lower bounds for $i(G)$ in terms of order, size or independence number. We obtain improved bounds for $i(G)$ on restricted graph classes such as the bipartite graphs, unicyclic graphs, regular graphs and claw-free graphs.
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