### Abstract

Atomic walk counts (awc's) of order k(k ≥ 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 ≤ m ≤ k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A^{-1} does not exist, awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.

Original language | English |
---|---|

Pages (from-to) | 1110-1114 |

Number of pages | 5 |

Journal | Journal of Chemical Information and Computer Sciences |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 2003 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Chemical Information and Computer Sciences*,

*43*(4), 1110-1114. https://doi.org/10.1021/ci025655t

**Atomic walk counts of negative order.** / Lukovits, I.; Trinajstić, Nenad.

Research output: Contribution to journal › Article

*Journal of Chemical Information and Computer Sciences*, vol. 43, no. 4, pp. 1110-1114. https://doi.org/10.1021/ci025655t

}

TY - JOUR

T1 - Atomic walk counts of negative order

AU - Lukovits, I.

AU - Trinajstić, Nenad

PY - 2003/7

Y1 - 2003/7

N2 - Atomic walk counts (awc's) of order k(k ≥ 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 ≤ m ≤ k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A-1 does not exist, awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.

AB - Atomic walk counts (awc's) of order k(k ≥ 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 ≤ m ≤ k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A-1 does not exist, awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.

UR - http://www.scopus.com/inward/record.url?scp=0042199133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042199133&partnerID=8YFLogxK

U2 - 10.1021/ci025655t

DO - 10.1021/ci025655t

M3 - Article

C2 - 12870900

AN - SCOPUS:0042199133

VL - 43

SP - 1110

EP - 1114

JO - Journal of Chemical Information and Modeling

JF - Journal of Chemical Information and Modeling

SN - 1549-9596

IS - 4

ER -