The Hyper-Wiener Index of Trees of Order n with Diameter d
The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/7241349 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549868336316416 |
|---|---|
| author | Gaixiang Cai Guidong Yu Jinde Cao Ahmad Alsaedi Fuad Alsaadi |
| author_facet | Gaixiang Cai Guidong Yu Jinde Cao Ahmad Alsaedi Fuad Alsaadi |
| author_sort | Gaixiang Cai |
| collection | DOAJ |
| description | The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of the two vertices u and v in the graph G. In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs. |
| format | Article |
| id | doaj-art-8f91b756dcf74a36b53bbcee5adea446 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8f91b756dcf74a36b53bbcee5adea4462025-02-03T06:08:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/72413497241349The Hyper-Wiener Index of Trees of Order n with Diameter dGaixiang Cai0Guidong Yu1Jinde Cao2Ahmad Alsaedi3Fuad Alsaadi4School of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, ChinaSchool of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, ChinaDepartment of Mathematics, Southeast University, Nanjing, Jiangsu 210096, ChinaFaculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of the two vertices u and v in the graph G. In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs.http://dx.doi.org/10.1155/2016/7241349 |
| spellingShingle | Gaixiang Cai Guidong Yu Jinde Cao Ahmad Alsaedi Fuad Alsaadi The Hyper-Wiener Index of Trees of Order n with Diameter d Discrete Dynamics in Nature and Society |
| title | The Hyper-Wiener Index of Trees of Order n with Diameter d |
| title_full | The Hyper-Wiener Index of Trees of Order n with Diameter d |
| title_fullStr | The Hyper-Wiener Index of Trees of Order n with Diameter d |
| title_full_unstemmed | The Hyper-Wiener Index of Trees of Order n with Diameter d |
| title_short | The Hyper-Wiener Index of Trees of Order n with Diameter d |
| title_sort | hyper wiener index of trees of order n with diameter d |
| url | http://dx.doi.org/10.1155/2016/7241349 |
| work_keys_str_mv | AT gaixiangcai thehyperwienerindexoftreesofordernwithdiameterd AT guidongyu thehyperwienerindexoftreesofordernwithdiameterd AT jindecao thehyperwienerindexoftreesofordernwithdiameterd AT ahmadalsaedi thehyperwienerindexoftreesofordernwithdiameterd AT fuadalsaadi thehyperwienerindexoftreesofordernwithdiameterd AT gaixiangcai hyperwienerindexoftreesofordernwithdiameterd AT guidongyu hyperwienerindexoftreesofordernwithdiameterd AT jindecao hyperwienerindexoftreesofordernwithdiameterd AT ahmadalsaedi hyperwienerindexoftreesofordernwithdiameterd AT fuadalsaadi hyperwienerindexoftreesofordernwithdiameterd |