A theorem on graph valence shells

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Recently Randić [1] has proposed a set of new graph invariants: the graph valence shells. A valence shell s(u)k is the sum of valences (degrees) of all vertices placed at distance k - 1 from vertex u. The graph valence shell sk, is the sum of valence shells s(u)k. Consider an acyclic graph T. It has been proved that sk = pk - 1 + Pk, where pk denotes the number of paths of length k in T.

Original languageEnglish
Pages (from-to)279-286
Number of pages8
Publication statusPublished - Dec 1 2001


ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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