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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.08213 |
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| _version_ | 1866911284138606592 |
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| author | Hamoud, Jasem Kornosov, Artem |
| author_facet | Hamoud, Jasem Kornosov, Artem |
| contents | In this paper, we presented a study of topological indices on trees, where we show a relationship with irregularity of Albertson index and minimum, maximum degrees $δ,Δ$ of graph $G$, where contribute vital roles in determining connection, shading, component incorporation, and realisability where well-known Albertson index as: $\operatorname{irr}(G)=\sum_{uv\in E(G)}\lvert d_u(G)-d_v(G) \rvert$. The sigma index on trees that we introduced as $σ(T)=(d_1-1)^3+\sum_{i=1}^{3}(d_i-1)(d_i-2)+(d_3-1)^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degree Sequence of Albertson and $σ$-Indices on Trees of Order $n\geqslant 3$ Hamoud, Jasem Kornosov, Artem Combinatorics 05C05, 05C12, 05C35, 68R10 G.2.2 In this paper, we presented a study of topological indices on trees, where we show a relationship with irregularity of Albertson index and minimum, maximum degrees $δ,Δ$ of graph $G$, where contribute vital roles in determining connection, shading, component incorporation, and realisability where well-known Albertson index as: $\operatorname{irr}(G)=\sum_{uv\in E(G)}\lvert d_u(G)-d_v(G) \rvert$. The sigma index on trees that we introduced as $σ(T)=(d_1-1)^3+\sum_{i=1}^{3}(d_i-1)(d_i-2)+(d_3-1)^3$. |
| title | Degree Sequence of Albertson and $σ$-Indices on Trees of Order $n\geqslant 3$ |
| topic | Combinatorics 05C05, 05C12, 05C35, 68R10 G.2.2 |
| url | https://arxiv.org/abs/2506.08213 |