Now showing items 1-10 of 13
On tactical configurations with no four-cycles
An improved lower bound is given for the band sizes of tactical configurations of rank exceeding two having no 4-cycles. This bound is applied to find an optimal configuration with certain specified parameters. A formula ...
The communication problem on graphs and digraphs
The study of shape transformation after D'Arcy Thompson
On the number of unique subgraphs
Entringer and Erdos introduced the concept of a unique subgraph of a given graph G and obtained a lower bound for the maximum number of unique subgraphs in any n-point graph, which we now improve.
Linear machinery for morphological distortion
In 1917 D'Arcy Thompson reduced the problem of comparing two homologous shapes to the construction and depiction of a mathematical distortion in the plane. Attempts at algorithms for this computation, found mostly in the ...
The number of caterpillars
A caterpillar is a tree which metamorphoses into a path when its cocoon of endpoints is removed. The number of nonisomorphic caterpillars with n+4 points is 2n + 2[n/2]. This neat formula is proved in two ways: first, as ...
The graphs with only self-dual signings
Given a graph G, it is possible to attach positive and negative signs to its lines only, to its points only, or to both. The resulting structures are called respectively signed graphs, marked graphs and nets. The dual of ...
The cutting center theorem for trees
We introduce the cutting number of a point of a connected graph as a natural measure of the extent to which the removal of that point disconnects the graph. The cutting center of the graph is the set of points of maximum ...
Correction to C. J. Swain's program for interpolating irregularly spaced data
Graph theory 1736-1936 : By N. L. Biggs, E. K. Lloyd, and R. J. Wilson. Oxford (Clarendon Press). 1976. 239 pp. $27.85