“Hyper-Wiener index”的意思、由来-开放百科全书

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Hyper-Wiener index

释义

Example
References

In chemical graph theory, the hyper-Wiener index or hyper-Wiener number is a topological index of a molecule, used in biochemistry. The hyper-Wiener index is a generalization introduced by Milan Randić

^[1] of the concept of the Wiener index, introduced by Harry Wiener. The hyper-Wiener index of a connected graph G is defined by

where d(u,v) is the distance between vertex u and v.

Hyper-Wiener index as topological index assigned to G = (V,E) is based on the distance function which is invariant under the action of the automorphism group of G.

Example

One-pentagonal carbon nanocone which is an infinite symmetric graph, consists of one pentagon as its core surrounded by layers of hexagons. If there are n layers, then the graph of the molecules is denoted by G_n.

we have the following explicit formula for hyper-Wiener index of one-pentagonal carbon nanocone,^[2]

References

1. ^{{citation | last1 = Randic | first1 = M. | doi = 10.1016/0009-2614(93)87094-J | issue = 10 | journal = Chemical Physics Letters | pages = 478-483 | title = Novel molecular descriptor for structure—property studies | volume = 211 | year = 1993| bibcode = 1993CPL...211..478R }}.
2. ^{{citation | last1 = Darafsheh| first1 = M. R. | last2 = Khalifeh| first2 = M. H. | last3 = Jolany| first3 = H. | doi = 10.2174/15734137113090990061 | issue = 4 | journal = Current Nanoscience | pages = 557-560 | title = The Hyper-Wiener Index of One-pentagonal Carbon Nanocone | volume = 9 | year = 2013| arxiv = 1212.4411}}.

1 : Graph invariants

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