On strict Semibound Graphs of Posets

For a poset \( P = (V(P), \leq_P) \), the strict semibound graph of \( P \) is the graph \( ssb(P) \) on \( V(ssb(P)) = V(P) \) for which vertices \( u \) and \( v \) of \( ssb(P) \) are adjacent if and only if \( u \neq v \) and there exists an element \( x \in V(P) \) distinct from \( u \) and \( v \) such that \( x \leq_P u,v \) or \( u,v \leq_P x \). We prove that a poset \( P \) is connected if