Computing bounds for the general sum-connectivity index of some graph operations
Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). Denote by \(d_{G}(u)\) the degree of a vertex \(u\in V(G)\). The general sum-connectivity index of \(G\) is defined as \(\chi_{\alpha}(G)=\sum_{u_{1}u_2\in E(G)}(d_{G}(u_1)+d_{G}(u_2))^{\alpha}\), where \(\alpha\) is a real number....
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2020
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/281 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543034104086528 |
|---|---|
| author | Akhter, S. Farooq, R. |
| author_facet | Akhter, S. Farooq, R. |
| author_sort | Akhter, S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-07-08T07:13:20Z |
| description | Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). Denote by \(d_{G}(u)\) the degree of a vertex \(u\in V(G)\). The general sum-connectivity index of \(G\) is defined as \(\chi_{\alpha}(G)=\sum_{u_{1}u_2\in E(G)}(d_{G}(u_1)+d_{G}(u_2))^{\alpha}\), where \(\alpha\) is a real number. In this paper, we compute the bounds for general sum-connectivity index of several graph operations. These operations include corona product, cartesian product, strong product, composition, join, disjunction and symmetric difference of graphs. We apply the obtained results to find the bounds for the general sum-connectivity index of some graphs of general interest. |
| first_indexed | 2025-12-02T15:40:03Z |
| format | Article |
| id | admjournalluguniveduua-article-281 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:03Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-2812020-07-08T07:13:20Z Computing bounds for the general sum-connectivity index of some graph operations Akhter, S. Farooq, R. general sum-connectivity index, Randi\'c index, corona product, strong product, symmetric difference 05C76, 05C07 Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). Denote by \(d_{G}(u)\) the degree of a vertex \(u\in V(G)\). The general sum-connectivity index of \(G\) is defined as \(\chi_{\alpha}(G)=\sum_{u_{1}u_2\in E(G)}(d_{G}(u_1)+d_{G}(u_2))^{\alpha}\), where \(\alpha\) is a real number. In this paper, we compute the bounds for general sum-connectivity index of several graph operations. These operations include corona product, cartesian product, strong product, composition, join, disjunction and symmetric difference of graphs. We apply the obtained results to find the bounds for the general sum-connectivity index of some graphs of general interest. Lugansk National Taras Shevchenko University Higher Education Commission of Pakistan 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/281 10.12958/adm281 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/281/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/281/115 Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | general sum-connectivity index Randi\'c index corona product strong product symmetric difference 05C76 05C07 Akhter, S. Farooq, R. Computing bounds for the general sum-connectivity index of some graph operations |
| title | Computing bounds for the general sum-connectivity index of some graph operations |
| title_full | Computing bounds for the general sum-connectivity index of some graph operations |
| title_fullStr | Computing bounds for the general sum-connectivity index of some graph operations |
| title_full_unstemmed | Computing bounds for the general sum-connectivity index of some graph operations |
| title_short | Computing bounds for the general sum-connectivity index of some graph operations |
| title_sort | computing bounds for the general sum-connectivity index of some graph operations |
| topic | general sum-connectivity index Randi\'c index corona product strong product symmetric difference 05C76 05C07 |
| topic_facet | general sum-connectivity index Randi\'c index corona product strong product symmetric difference 05C76 05C07 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/281 |
| work_keys_str_mv | AT akhters computingboundsforthegeneralsumconnectivityindexofsomegraphoperations AT farooqr computingboundsforthegeneralsumconnectivityindexofsomegraphoperations |