Some Concepts of Graph Theory

On some applications of graph theory, I

In a series of papers, of which the present one is Part I, it is shown that solutions to a variety of problems in distance geoinetry, potential theory and theory of metric spaces arc provided by appropriate applications of graph theoretic results. §1 In what follows we are going to discuss systematic applications of graph theory-among others-to geometry, to potential theory, and to the theory o...

On Some Applications of Graph Theory Iii

1 . In the first and second parts of this sequence we dealt with applications of graph theory to distance distribution in certain sets in euclidean spaces, to potential theory, to estimations of the transfinite diameter [1] and to value distribution of "triangle functionals" (e.g. perimeter, area of triangles) [2] . The basic tool is provided in all these applications by the result formulated a...

Some Concepts in Probability and Information Theory

On Some Applications of Graph Theory, II

For m = 2 we get the graphs. n is again the order of the m-graph; the meaning of m-subgraphs, complete m-graphs is obvious. We shall deal especially with the case m = 3, i.e. with the case of trigraphs, though the geometrical problems we are dealing with have natural analogues (and also problems of new type) for higher dimensions, and these involve m-graphs with general m’s, Let A,, A,, A, be t...

Graph-set analysis of hydrogen-bond patterns: some mathematical concepts.

To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other intermolecular interactions a number of mathematical concepts and tools are defined, developed and demonstrated. Following a review of the basic definitions and uses of graph sets, the directional properties of hydrogen bonds are now included in the...