AL DEZA MICHEL-MARIE ET (EN) — SCALE-ISOMETRIC POLYTOPAL GRAPHS IN HYPERCUBES AND CUBIC LATTICES

SCALE-ISOMETRIC POLYTOPAL GRAPHS IN HYPERCUBES AND CUBIC LATTICES краткое содержание

SCALE-ISOMETRIC POLYTOPAL GRAPHS IN HYPERCUBES AND CUBIC LATTICES - описание и краткое содержание, автор AL DEZA MICHEL-MARIE ET (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

This monograph identifies polytopes that are “combinatorially ℓ1-embeddable”, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to “ℓ2-prominent” affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability — the main unifying question, to which those lists are subjected — is presented with the minimum of technicalities.Contents:Introduction: Graphs and Their Scale-Isometric EmbeddingAn Example: Embedding of FullerenesRegular Tilings and HoneycombsSemi-regular Polyhedra and Relatives of Prisms and AntiprismsTruncation, Capping and Chamfering92 Regular-faced (not Semi-regular) PolyhedraSemi-regular and Regular-faced n-Polytopes, n ≥ 4Polycycles and Other Chemically Relevant GraphsPlane TilingsUniform Partitions of 3-Space and RelativesLattices, Bi-lattices and TilesSmall PolyhedraBifaced PolyhedraSpecial ℓ1-graphsSome Generalization of ℓ1-embeddingReadership: Researchers in combinatorics and graph theory.