Topological Indices With Degree Sequence $\mathscr{D}$ of Tree
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917143225827328 |
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| author | Hamoud, Jasem Abdullah, Duaa |
| author_facet | Hamoud, Jasem Abdullah, Duaa |
| contents | In this paper, we refer to a asymptotic degree sequence as $\mathscr{D}=(d_1,d_2,\dots,d_n)$. The examination of topological indices on trees gives us a general overview through bounds to find the maximum and minimum bounds which reflect the maximum and minimum number of edges incident to every vertex in the graph, Albertson index known as $\sum_{uv\in E(G)}\lvert d_u(G)-d_v(G) \rvert$, Sigma index $σ(G)$ among $\mathscr{D}$ of tree $T$ when $d_n\geqslant \dots \geqslant d_1$. According to the first zegrb we show for a degree sequence of order $n=4$, $\operatorname{irr}(T)=M_1(T)^2-2\sqrt{M_1(T)}+\sum_{i=1}^4\left|x_i-x_{i+1}\right|-(b+c)-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Indices With Degree Sequence $\mathscr{D}$ of Tree Hamoud, Jasem Abdullah, Duaa Combinatorics 05C20, 05C69, 68R10 G.2.2 In this paper, we refer to a asymptotic degree sequence as $\mathscr{D}=(d_1,d_2,\dots,d_n)$. The examination of topological indices on trees gives us a general overview through bounds to find the maximum and minimum bounds which reflect the maximum and minimum number of edges incident to every vertex in the graph, Albertson index known as $\sum_{uv\in E(G)}\lvert d_u(G)-d_v(G) \rvert$, Sigma index $σ(G)$ among $\mathscr{D}$ of tree $T$ when $d_n\geqslant \dots \geqslant d_1$. According to the first zegrb we show for a degree sequence of order $n=4$, $\operatorname{irr}(T)=M_1(T)^2-2\sqrt{M_1(T)}+\sum_{i=1}^4\left|x_i-x_{i+1}\right|-(b+c)-1$. |
| title | Topological Indices With Degree Sequence $\mathscr{D}$ of Tree |
| topic | Combinatorics 05C20, 05C69, 68R10 G.2.2 |
| url | https://arxiv.org/abs/2503.12909 |