On distance two graphs of upper bound graphs

For a poset P = ( X , ≤ ) , the upper bound graph (UB-graph) of P is the graph U = ( X , E U ) , where u v ∈ E U if and only if u ≠ v and there exists m ∈ X such that u , v ≤ m . For a graph G , the distance two graph D S 2 ( G ) is the graph with vertex set V ( D S 2 ( G ) ) = V ( G ) and u , v ∈ V ( D S 2 ( G ) ) are adjacent if and only if d G ( u , v ) = 2 . In this paper, we deal with distance two graphs of upper bound graphs. We obtain a characterization of distance two graphs of split upper bound graphs.