### Abstract

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 s_{k}, is the sum of valence shells s(u)_{k}. Consider an acyclic graph T. It has been proved that s_{k} = p_{k - 1} + P_{k}, where p_{k} denotes the number of paths of length k in T.

Original language | English |
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Pages (from-to) | 279-286 |

Number of pages | 8 |

Journal | Match |

Volume | 44 |

Publication status | Published - Dec 1 2001 |

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### ASJC Scopus subject areas

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