Abstract: | We study planar graphs embedded in the plane that have chemical applications: the degrees of all vertices are 3 or 2, all
internal faces but one or two arer-gons, and each internal face is a simply connected domain. For wide classes of such graphs, we solve the existence problem
for embeddings of the graph metric on the vertices in multidimensional cubes or cubical lattices preserving or doubling all
the distances. Incidentally we present a complete classification of some interesting families of such graphs.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 339–352, September, 2000. |