Maximum genus and maximum nonseparating independent set of a 3-regular graph (Q1377685)

Let \(G\) be a connected graph with vertex set \(V\). A set \(J\subseteq V\) is called a nonseparating independent set (nsis) if \(J\) is an independent set of \(G\) and \(G-J\) is connected. The nsis number of \(G\), \(z(G)\), is the maximum cardinality that an nsis for \(G\) can attain. The authors show that, for \(G\) a 3-regular connected graph, the maximum genus is equal to \(z(G)\). This is then used to obtain several new results about the maximum genus parameter.