L1-embeddability under the edge-gluing operation on graphs

A graph is an l 1 -graph if its vertices can be labeled by binary vectors in such a way that the Hamming distance between the binary addresses is, up to scale, the distance in the graph between the corresponding vertices. In this note, we study when the result of gluing two l 1 -graphs along an edge is an l 1 -graph. If at least one of the constituent graphs is bipartite, then the resulting graph is also an l 1 -graph. For two nonbipartite l 1 -graphs, this is not always the case.