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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.

The boolean distance between two points x and y of a connected graph G is defined as the set of all points on all paths joining x and y in G (O if X = y). It is determined in terms of the block-cutpoint graph of G, and ...

Consider the following two graphs M and N, both with vertex set Z x Z, where Z is the set of all integers. In M, two vertices are adjacent when their euclidean distance is 1, while in N, adjacency is obtained when the ...

Quantum chemical reaction graphs defined on multidimensional potential energy hypersurfaces are embedded on two-dimensional orientable surfaces. Topological invariants of these graphs and those of the embedding two-dimensional ...

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 ...

Fractal geometric parameters were employed to assess the morphometric viability of traditionally defined physiographic provinces using relatively coarse 30-arc-second digital elevation models (DEM) within 1[deg] x 1[deg] ...