# Does this kind of graph formed from a linear collection of bipartite subgraphs have a name?

In investigating an earlier question I proposed to this site, I came across a bipartite graph with certain properties. I briefly searched for other bipartite graph questions but didn't find anything similar.

Consider a graph $G=(V,E)$ such that it's vertices can be partitioned into subsets $\{U_1,\dotsc,U_n\}$ where for any edge $(a,b) \in E$ we have that if $a \in U_k$ then $b \in U_{k+1}$. Under this condition any adjacent pair of vertex subsets $U_k$ and $U_{k+1}$ (for $1 \leq k<n$) induce a bipartite subgraph. Additionally, $G$ can be depicted as a single bipartite graph by grouping the vertices $\{U_1, U_3, \dotsc\}$ and $\{U_2, U_4, \dotsc\}$ into the two separate parts.

Does this particular type of graph have a name, or any practical application or special properties? If so, has it been studied to any extent?