Scale-isometric polytopal graphs in hypercubes and cubic lattices - polytopes in hypercubes and Zn
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منابع مشابه
On cubic and edge-critical isometric subgraphs of hypercubes
All cubic partial cubes (i.e., cubic isometric subgraphs of hypercubes) up to 30 vertices and all edge-critical partial cubes up to 14 vertices are presented. The lists of graphs were confirmed by computer search to be complete. Non-trivial cubic partial cubes on 36, 42, and 48 vertices are also constructed.
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We review the regular tilings of d-sphere, Euclidean d-space, hyperbolic d-space and Coxeter’s regular hyperbolic honeycombs (with infinite or star-shaped cells or vertex figures) with respect of possible embedding, isometric up to a scale, of their skeletons into a m-cube or m-dimensional cubic lattice. In section 2 the last remaining 2-dimensional case is decided: for any odd m ≥ 7, star-hone...
متن کاملSpin systems on hypercubic Bethe lattices: A Bethe-Peierls approach
We study spin systems on Bethe lattices constructed from ddimensional hypercubes. Although these lattices are not tree-like, and therefore closer to real cubic lattices than Bethe lattices or regular random graphs, one can still use the Bethe-Peierls method to derive exact equations for the magnetization and other thermodynamic quantities. We compute phase diagrams for ferromagnetic Ising model...
متن کاملIsometric embeddings of subdivided connected graphs into hypercubes
Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first been investigated by Graham and Pollack [R.L. Graham, H. Pollack, On the addressing problem for loop switching, Bell System Technol. J. 50 (1971) 2495–2519; and D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263–267]. Several papers followed with various characteri...
متن کاملA Poset-based Approach to Embedding Median Graphs in Hypercubes and Lattices
A median graph G is a graph where, for any three vertices u, v and w, there is a unique node that lies on a shortest path from u to v, from u to w, and from v to w. While not obvious from the definition, median graphs are partial cubes; that is, they can be isometrically embedded in hypercubes and, consequently, in integer lattices. The isometric and lattice dimensions of G, denoted as dimI(G) ...
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تاریخ انتشار 2004