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A set of vertices in a graph is called independent if no two vertices of theset are connected by an edge. In this paper we use the state matrix recursionalgorithm, developed by Oh, to enumerate independent vertex sets in a gridgraph and even further to provide the generating function with respect to thenumber of vertices. We also enumerate bipartite independent vertex sets in agrid graph. The asymptotic behavior of their growth rates is presented.

Enumerating independent vertex sets in grid graphs