Bounds on Trees with Topological Indices Among Degree Sequence
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910977322123264 |
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| author | Hamoud, Jasem Belov-Kanel, Alexei Abdullah, Duaa |
| author_facet | Hamoud, Jasem Belov-Kanel, Alexei Abdullah, Duaa |
| contents | In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two topological indices, and we show that the Albertson index $\irr(T)$ and the first Zagreb index $M_1(T)$ satisfy the association \[ \operatorname{irr}(T)=d_1^2+d_n^2+(n-2)\left(\frac{Δ+ δ}{2}\right)^2+\sum_{i=2}^{n-1} d_i+d_n - d_1-2n-2.\] Our goal of this paper is provide a topological indices, Albertson index, Sigma index among a degree sequence $\mathscr{D}=(d_1,\dots,d_n)$ where it is non-increasing and non-decreasing of tree $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on Trees with Topological Indices Among Degree Sequence Hamoud, Jasem Belov-Kanel, Alexei Abdullah, Duaa Combinatorics 05C05, 05C12, 05C35, 68R10 G.2.2 In this paper, we investigate The relationship between the Albertson index and the first Zagreb index for trees. For a tree $T=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges, we provide several bounds and exact formulas for these two topological indices, and we show that the Albertson index $\irr(T)$ and the first Zagreb index $M_1(T)$ satisfy the association \[ \operatorname{irr}(T)=d_1^2+d_n^2+(n-2)\left(\frac{Δ+ δ}{2}\right)^2+\sum_{i=2}^{n-1} d_i+d_n - d_1-2n-2.\] Our goal of this paper is provide a topological indices, Albertson index, Sigma index among a degree sequence $\mathscr{D}=(d_1,\dots,d_n)$ where it is non-increasing and non-decreasing of tree $T$. |
| title | Bounds on Trees with Topological Indices Among Degree Sequence |
| topic | Combinatorics 05C05, 05C12, 05C35, 68R10 G.2.2 |
| url | https://arxiv.org/abs/2505.12518 |