Diminished Sombor matrix, spectral radius, and energy of the graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909730505490432 |
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| author | Movahedi, F. |
| author_facet | Movahedi, F. |
| contents | Consider a simple graph $G$ with vertex set $V = \{v_1, v_2, \ldots, v_n\}$ and edge set $E$. The diminished Sombor matrix $M_{DS}(G)$ is constructed such that its $(i, j)$ entry is $\frac{\sqrt{d_i^2+d_j^2}}{d_i+d_j}$ if vertices $v_iv_j \in E$, and $0$ otherwise, where $d_i$ represents the degree of vertex $v_i$. In this paper, we establish sharp bounds for the spectral radius, and energy of the Sombor matrix of graphs and identify the graphs that attain these extremal values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diminished Sombor matrix, spectral radius, and energy of the graphs Movahedi, F. Combinatorics 05C09, 05C92, 05C90 Consider a simple graph $G$ with vertex set $V = \{v_1, v_2, \ldots, v_n\}$ and edge set $E$. The diminished Sombor matrix $M_{DS}(G)$ is constructed such that its $(i, j)$ entry is $\frac{\sqrt{d_i^2+d_j^2}}{d_i+d_j}$ if vertices $v_iv_j \in E$, and $0$ otherwise, where $d_i$ represents the degree of vertex $v_i$. In this paper, we establish sharp bounds for the spectral radius, and energy of the Sombor matrix of graphs and identify the graphs that attain these extremal values. |
| title | Diminished Sombor matrix, spectral radius, and energy of the graphs |
| topic | Combinatorics 05C09, 05C92, 05C90 |
| url | https://arxiv.org/abs/2508.06531 |