### 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 - 2001 |

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### ASJC Scopus subject areas

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

### Cite this

**A theorem on graph valence shells.** / Lukovits, I.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A theorem on graph valence shells

AU - Lukovits, I.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035746463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035746463&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035746463

VL - 44

SP - 279

EP - 286

JO - Match

JF - Match

SN - 0340-6253

ER -