### Abstract

The detour index w is the sum of all entries in the upper triangle of the detour matrix Δ, where the ij-th entry Δ_{ij} denotes the length of the longest path between vertices i and j of the underlying graph. The Wiener index W and w are equivalent for acyclic structures, but are different in cycle-containing graphs. Similarly the hyper-Wiener index Γ and its analogue the hyper-detour index γ are equivalent in acyclic structures and are different in cyclic structures. Several formulas were derived for w and γ- Excellent correlations between boiling points and the composite indices (Ww)^{1/8} and (Γγ)^{1/10} were found in a series consisting of 77 cyclic and acyclic alkanes.

Original language | English |
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Pages (from-to) | 873-882 |

Number of pages | 10 |

Journal | Croatica Chemica Acta |

Volume | 69 |

Issue number | 3 |

Publication status | Published - Nov 1996 |

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### ASJC Scopus subject areas

- Chemistry(all)

### Cite this

**The Detour Index.** / Lukovits, I.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - The Detour Index

AU - Lukovits, I.

PY - 1996/11

Y1 - 1996/11

N2 - The detour index w is the sum of all entries in the upper triangle of the detour matrix Δ, where the ij-th entry Δij denotes the length of the longest path between vertices i and j of the underlying graph. The Wiener index W and w are equivalent for acyclic structures, but are different in cycle-containing graphs. Similarly the hyper-Wiener index Γ and its analogue the hyper-detour index γ are equivalent in acyclic structures and are different in cyclic structures. Several formulas were derived for w and γ- Excellent correlations between boiling points and the composite indices (Ww)1/8 and (Γγ)1/10 were found in a series consisting of 77 cyclic and acyclic alkanes.

AB - The detour index w is the sum of all entries in the upper triangle of the detour matrix Δ, where the ij-th entry Δij denotes the length of the longest path between vertices i and j of the underlying graph. The Wiener index W and w are equivalent for acyclic structures, but are different in cycle-containing graphs. Similarly the hyper-Wiener index Γ and its analogue the hyper-detour index γ are equivalent in acyclic structures and are different in cyclic structures. Several formulas were derived for w and γ- Excellent correlations between boiling points and the composite indices (Ww)1/8 and (Γγ)1/10 were found in a series consisting of 77 cyclic and acyclic alkanes.

UR - http://www.scopus.com/inward/record.url?scp=0001023682&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001023682&partnerID=8YFLogxK

M3 - Article

VL - 69

SP - 873

EP - 882

JO - Croatica Chemica Acta

JF - Croatica Chemica Acta

SN - 0011-1643

IS - 3

ER -