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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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2020
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/281 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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