Further results on the lower bound on reduced Zagreb index of trees
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913012072316928 |
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| author | Bašić, Milan Ilić, Aleksandar |
| author_facet | Bašić, Milan Ilić, Aleksandar |
| contents | For a graph $G$, the general reduced second Zagreb index is defined as $$GRM_λ(G) = \sum_{uv \in E} (deg(u) + λ) (deg(v) + λ),$$ where $λ$ is an arbitrary real number and $deg (v)$ is the degree of the vertex $v$.
In this paper, we extend and correct the equality results from [N. Dehgardia, S. Klav\v zar, {\it Improved lower bounds on the general reduced second Zagreb index of trees}, preprint (2023)] regarding the minimal value of $GRM_λ$ for $λ\geq -1$ among trees with $n$ vertices and a maximal degree $Δ$. Furthermore, we complement these results with two distinct approaches to determine the minimum value of the general reduced second Zagreb index for molecular trees with $Δ= 3$ and $Δ= 4$ in $λ= -2$, and characterize the extremal trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Further results on the lower bound on reduced Zagreb index of trees Bašić, Milan Ilić, Aleksandar Combinatorics Discrete Mathematics 05C09, 11A07, 90C27, 90C10 For a graph $G$, the general reduced second Zagreb index is defined as $$GRM_λ(G) = \sum_{uv \in E} (deg(u) + λ) (deg(v) + λ),$$ where $λ$ is an arbitrary real number and $deg (v)$ is the degree of the vertex $v$. In this paper, we extend and correct the equality results from [N. Dehgardia, S. Klav\v zar, {\it Improved lower bounds on the general reduced second Zagreb index of trees}, preprint (2023)] regarding the minimal value of $GRM_λ$ for $λ\geq -1$ among trees with $n$ vertices and a maximal degree $Δ$. Furthermore, we complement these results with two distinct approaches to determine the minimum value of the general reduced second Zagreb index for molecular trees with $Δ= 3$ and $Δ= 4$ in $λ= -2$, and characterize the extremal trees. |
| title | Further results on the lower bound on reduced Zagreb index of trees |
| topic | Combinatorics Discrete Mathematics 05C09, 11A07, 90C27, 90C10 |
| url | https://arxiv.org/abs/2604.06044 |