## We enumerate, up to isomorphism, several classes of labeled vertex-transitive digraphs with a prime number of vertices. There are many unsolvedi enumeration problems stated in [S]. Recently, Robinson in [8] posed more enumeration problems. Here, we give some partial answer to the problems posed
Numbering binary trees with labeled terminal vertices
β Scribed by F. James Rohlf
- Publisher
- Springer
- Year
- 1983
- Tongue
- English
- Weight
- 353 KB
- Volume
- 45
- Category
- Article
- ISSN
- 1522-9602
No coin nor oath required. For personal study only.
β¦ Synopsis
For each rooted binary tree with t labeled terminal vertices (leaves) a natural number can be assigned uniquely. Unrooted trees with t labeled terminal vertices and t-2 unlabeled internal vertices of degree 3 can also be numbered uniquely using the same convention. Rooted trees in which the heights of the internal vertices are rank ordered are also considered. Applications to problems in taxonomy are discussed.
π SIMILAR VOLUMES
If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span
## Abstract The __allyβreconstruction number__ of a graph __G__, allyβrn(__G__), is the minimum number of vertexβdeleted subgraphs required in order to identify __G__ up to isomorphism. In this paper, we show that allyβrn(__T__) = 3 for any tree __T__ with five or more vertices.
For an n-dimensional hypercube Q., the maximum number of degree-preserving vertices in a spanning tree is 2"jn if n = 2" for an integer M. (If n # 2", then the maximum number of degree-preserving vertices in a spanning tree is less than 2"/n.) We also construct a spanning tree of Qzm with maximum nu