Reformulated Zagreb Indices of Trees
Zagreb indices were reformulated in terms of the edge degrees instead of the vertex degrees. For a graph $G$, the first and second reformulated Zagreb indices are defined respectively as:$$EM_1(G)=\sum_{\varepsilon\in E(G)}d^2(\varepsilon), EM_2(G)=\sum_{\varepsilon,\varepsilon'\in E(G),\...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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University of Kashan
2024-12-01
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| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_114582_10a159ccec96295fb043722130466579.pdf |
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| Summary: | Zagreb indices were reformulated in terms of the edge degrees instead of the vertex degrees. For a graph $G$, the first and second reformulated Zagreb indices are defined respectively as:$$EM_1(G)=\sum_{\varepsilon\in E(G)}d^2(\varepsilon), EM_2(G)=\sum_{\varepsilon,\varepsilon'\in E(G),\,\varepsilon\sim \varepsilon'}d(\varepsilon)\,d(\varepsilon'),$$ where $d(\varepsilon)$ and $d(\varepsilon')$ denote the degree of the edges $\varepsilon$ and $\varepsilon'$ respectively, and $\varepsilon\sim \varepsilon'$ means that the edges $\varepsilon$ and $\varepsilon'$ are adjacent. In this paper, we obtain sharp lower bounds on the first and second reformulated Zagreb indices with a given number of vertices and maximum degree. Furthermore, we will determine the extremal trees that achieve these lower bounds. |
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| ISSN: | 2476-4965 |