Representing Graphs by Knuth Trees
暂无分享,去创建一个
ASSrRACT. 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.
[1] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .
[2] Donald E. Knuth,et al. The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition , 1997 .
[3] Frank Harary,et al. Graph Theory , 2016 .
[4] Herbert J. Bernstein,et al. Four high-level extensions of FORTRAN IV: SLIP, AMPPL-II, TREETRAN, SYMBOLANG, , 1972 .