Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

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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.A circuit C of a plane graph G is said to be alternating (or left-right circuit, or Petri walk, or zigzag) if every face of G is either disjoint with C, or shares with it exactly two consecutive edges. Clearly, any edge of G is covered by exactly two circuitsanbsp;...

Title:Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices
Author:M. Deza, Viatcheslav Grishukhin, Mikhail Shtogrin
Publisher:Imperial College Press - 2004


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