Delocalization Subgraph Section

[rapodaca]

• VB model makes graphs unequal even though they should be treated as equal
  • DIME
• the DS solution
  • encodes alternating single-double bond pattern as a perfect matching
  • maximum, maximal, perfect matching
• a node-induced subgraph over VB graph
  • unlabeled
  • possibly empty
  • encodes and therefore guarantees a perfect matching
  • corollary: every atom will be assigned a double bond
  • only node membership is specified
  • edge membership is deduced
• composition
  • atoms
  • C, N, O, P, S, unknown
  • selection
  • adding an atom to the DS
  • "selected atom", "selected atoms"
  • "induced bond", "induced bonds"
• bonds
  • by definition (node-induced) both terminals are members
• literature refers to "aromaticity"
  • not using that term because of its (imprecise) meaning in chemistry
• algorithmic fill/empty
  • every molecule expressed with a DS can also be expressed without it
  • in other words, 1:1 translation
  • fill algorithm
  • empty algorithm
  • aka "kekulization"
• examples
  • invent a notation for node/edge membership (color?, weight?)
  • graphics only
• error states
  • no perfect matching possible
  • to re-iterate: DS is just another way to express single/double bond layout