Representing Graphs by Knuth Trees

Abstract

By means of the :Knuth transform, arbitrary rooted trees may be represented compactly as binary trees. In this paper it is shown that the domain of this transform may be extended to a much wider class of graphs, while still maintaining its fundamental properties. Graphs, G, belonging to this extended domain are characterized first in terms of properties of an induced graph, G*, and then in terms of local properties of G itself. A classic kind of “forbidden” subgraph theorem characterizes nonrepresentable graphs. Finally, it is shown that any directed graph can be modified to make it representable under the transform. © 1975, ACM. All rights reserved.