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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 ...

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.

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 ...

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 ...

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 ...

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 ...