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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.10944 |
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| _version_ | 1866917481459744768 |
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| author | de Lima, Gabriel Roberto Silva Oliveira, Carla Silva Junior, João Domingos Gomes da Silva |
| author_facet | de Lima, Gabriel Roberto Silva Oliveira, Carla Silva Junior, João Domingos Gomes da Silva |
| contents | Let $G$ be a simple graph, $A(G)$ its adjacency matrix, and $D(G)$ its diagonal degree matrix. In 2022, \citeauthor{Wang2020} (\cite{Wang2020}) defined the family of matrices $L_α$ as the convex linear combination: \[ L_α(G) = αD(G) + (α- 1)A(G), \] where $α\in [0,1]$. The study of the spectrum of this family of matrices may provide a unified framework for analyzing the spectra of the adjacency, degree, and Laplacian matrices ($D(G) - A(G)$). In this work, we investigate the spectrum of $L_α$ under graph operations and within specific families of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of $\boldsymbol{L_α}-$matrices under graph operations de Lima, Gabriel Roberto Silva Oliveira, Carla Silva Junior, João Domingos Gomes da Silva Combinatorics 05C05 Let $G$ be a simple graph, $A(G)$ its adjacency matrix, and $D(G)$ its diagonal degree matrix. In 2022, \citeauthor{Wang2020} (\cite{Wang2020}) defined the family of matrices $L_α$ as the convex linear combination: \[ L_α(G) = αD(G) + (α- 1)A(G), \] where $α\in [0,1]$. The study of the spectrum of this family of matrices may provide a unified framework for analyzing the spectra of the adjacency, degree, and Laplacian matrices ($D(G) - A(G)$). In this work, we investigate the spectrum of $L_α$ under graph operations and within specific families of graphs. |
| title | Eigenvalues of $\boldsymbol{L_α}-$matrices under graph operations |
| topic | Combinatorics 05C05 |
| url | https://arxiv.org/abs/2605.10944 |