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Coordination sequences for root lattices and related graphs

Published/Copyright: July 28, 2010
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 212 Issue 4

Abstract

The coordination sequence sΛ(k) of a graph Λ counts the number of its vertices which have distance k from a given vertex, where the distance between two vertices is defined as the minimal number of bonds in any path connecting them. For a large class of graphs, including in particular the classical root lattices, we present the coordination sequences and their generating functions, summarizing and extending recent results of Conway and Sloane [1].

Published Online: 2010-7-28
Published in Print: 1997-4-1

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Articles in the same Issue

  1. Coordination sequences for root lattices and related graphs
  2. Diffuse scattering from periodic and aperiodic crystals
  3. Crystal optics of D-mannitol, C6H14O6: crystal growth, structure, basic physical properties, birefringence, optical activity, Faraday effect, electro-optic effects and model calculations
  4. Structure of γ-Bi2Sn2O7 by high temperature powder neutron diffraction
  5. Crystal structure of sodium squarate trihydrate, Na2C4O4 · 3H2O
  6. Crystal structure determination of barium Oxalate, BaC2O4 · 3.5 H2O/D2O
  7. Crystal structure of N,N′-dimethyldiethylenediammonium hexafluorosilicate dihydrate, C6H16N2SiF6 · 2H2O
  8. Crystal structure of L-arginine perchlorate, C6H16ClN4O6
  9. Crystal structure of bis(L-valine nitrate), C5H12N2O5
  10. Crystal structure of 6,8-methanoisoquinoline-5,6,7,8-tetrahydro-7,7-dimethyl-3-(2-pyridinyl)-(6R), C17H18N2
  11. Crystal structure of 6,8-methanoisoquinoline-5,6,7,8-tetrahydro-7,7-dimethyl-3-(2-pyridyl)-(6R), C17H18N2
  12. Crystal structure of (dicyclopentadienyltetramethyldisiloxan) (dimethyl-aminodimethylsilyl-cyclopentadienylsamarium(III), C23H36NOSi3Sm
  13. Crystal structure of 2-acetamido-1-O-acetyl-2-deoxy-3,4:5,6-di-O-isopropylidene-D)-mannitol, C16H27NO7
  14. Crystal structure of (1R,2S)-N-benzyl-N-[2-(tert-butoxycarbonylamino)-1-(furan-2-yl)-1-propyl]hydroxylamine, C19H26N2O4
  15. Crystal structure of (bis(diphenylphosphino)methane)bromo (tricarbonyl)manganese(I) diethylether solvate, (CH2(P(C6H5)2)2)Mn(CO)3Br · (C2H5)2O
https://doi.org/10.1524/zkri.1997.212.4.253

Articles in the same Issue

  1. Coordination sequences for root lattices and related graphs
  2. Diffuse scattering from periodic and aperiodic crystals
  3. Crystal optics of D-mannitol, C6H14O6: crystal growth, structure, basic physical properties, birefringence, optical activity, Faraday effect, electro-optic effects and model calculations
  4. Structure of γ-Bi2Sn2O7 by high temperature powder neutron diffraction
  5. Crystal structure of sodium squarate trihydrate, Na2C4O4 · 3H2O
  6. Crystal structure determination of barium Oxalate, BaC2O4 · 3.5 H2O/D2O
  7. Crystal structure of N,N′-dimethyldiethylenediammonium hexafluorosilicate dihydrate, C6H16N2SiF6 · 2H2O
  8. Crystal structure of L-arginine perchlorate, C6H16ClN4O6
  9. Crystal structure of bis(L-valine nitrate), C5H12N2O5
  10. Crystal structure of 6,8-methanoisoquinoline-5,6,7,8-tetrahydro-7,7-dimethyl-3-(2-pyridinyl)-(6R), C17H18N2
  11. Crystal structure of 6,8-methanoisoquinoline-5,6,7,8-tetrahydro-7,7-dimethyl-3-(2-pyridyl)-(6R), C17H18N2
  12. Crystal structure of (dicyclopentadienyltetramethyldisiloxan) (dimethyl-aminodimethylsilyl-cyclopentadienylsamarium(III), C23H36NOSi3Sm
  13. Crystal structure of 2-acetamido-1-O-acetyl-2-deoxy-3,4:5,6-di-O-isopropylidene-D)-mannitol, C16H27NO7
  14. Crystal structure of (1R,2S)-N-benzyl-N-[2-(tert-butoxycarbonylamino)-1-(furan-2-yl)-1-propyl]hydroxylamine, C19H26N2O4
  15. Crystal structure of (bis(diphenylphosphino)methane)bromo (tricarbonyl)manganese(I) diethylether solvate, (CH2(P(C6H5)2)2)Mn(CO)3Br · (C2H5)2O
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