Summary: We call a graph \(G\) a generalized split graph if there exists a core \(K\) of \(G\) such that \(V(G)\backslash V(K)\) is an independent set of \(G\). Let \(G\) be a generalized split graph with a partition \(V(G)=K\dot {\cup }S\), where \(K\) is a core of \(G\) and \(S\) is an independent set. We prove that \(G\) is end-regular if and only if for any \(a,b\in S\), \(\phi \in \operatorname {Aut}(K)\), the inclusion \(\phi (N(a))\subsetneqq N(b)\) doesn’t hold, and that \(G\) is end-orthodox if and only if \(G\) is end-regular and for any \(a,b\in S\), \(N(a)\neq N(b)\).