Minimum Variable Connectivity Index of Trees of a Fixed Order
The connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications. In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index. The variable connectivity index for...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3976274 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566214786809856 |
|---|---|
| author | Shamaila Yousaf Akhlaq Ahmad Bhatti Akbar Ali |
| author_facet | Shamaila Yousaf Akhlaq Ahmad Bhatti Akbar Ali |
| author_sort | Shamaila Yousaf |
| collection | DOAJ |
| description | The connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications. In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index. The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G. Soon after the innovation of the variable connectivity index, its various chemical applications have been reported in different papers. However, to the best of the authors’ knowledge, mathematical properties of the variable connectivity index, for γ>0, have not yet been discussed explicitly in any paper. The main purpose of the present paper is to fill this gap by studying this topological index in a mathematical point of view. More precisely, in this paper, we prove that the star graph has the minimum variable connectivity index among all trees of a fixed order n, where n≥4. |
| format | Article |
| id | doaj-art-749c51a24f6248dd80e525ff9576550f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-749c51a24f6248dd80e525ff9576550f2025-02-03T01:04:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/39762743976274Minimum Variable Connectivity Index of Trees of a Fixed OrderShamaila Yousaf0Akhlaq Ahmad Bhatti1Akbar Ali2Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanDepartment of Mathematics, Faculty of Science, University of Ha’il, Ha’il, Saudi ArabiaThe connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications. In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index. The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G. Soon after the innovation of the variable connectivity index, its various chemical applications have been reported in different papers. However, to the best of the authors’ knowledge, mathematical properties of the variable connectivity index, for γ>0, have not yet been discussed explicitly in any paper. The main purpose of the present paper is to fill this gap by studying this topological index in a mathematical point of view. More precisely, in this paper, we prove that the star graph has the minimum variable connectivity index among all trees of a fixed order n, where n≥4.http://dx.doi.org/10.1155/2020/3976274 |
| spellingShingle | Shamaila Yousaf Akhlaq Ahmad Bhatti Akbar Ali Minimum Variable Connectivity Index of Trees of a Fixed Order Discrete Dynamics in Nature and Society |
| title | Minimum Variable Connectivity Index of Trees of a Fixed Order |
| title_full | Minimum Variable Connectivity Index of Trees of a Fixed Order |
| title_fullStr | Minimum Variable Connectivity Index of Trees of a Fixed Order |
| title_full_unstemmed | Minimum Variable Connectivity Index of Trees of a Fixed Order |
| title_short | Minimum Variable Connectivity Index of Trees of a Fixed Order |
| title_sort | minimum variable connectivity index of trees of a fixed order |
| url | http://dx.doi.org/10.1155/2020/3976274 |
| work_keys_str_mv | AT shamailayousaf minimumvariableconnectivityindexoftreesofafixedorder AT akhlaqahmadbhatti minimumvariableconnectivityindexoftreesofafixedorder AT akbarali minimumvariableconnectivityindexoftreesofafixedorder |