New results on $B_α$-eigenvalues of a graph
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908602082525184 |
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| author | Pastén, Germain Oliveira, Carla Silva Junior, João Domingos G. da Silva Justel, Claudia M. |
| author_facet | Pastén, Germain Oliveira, Carla Silva Junior, João Domingos G. da Silva Justel, Claudia M. |
| contents | Let $G$ be a graph with adjacency matrix $A(G)$ and Laplacian matrix $L(G)$. In 2024, Samanta \textit{et} \textit{al.} defined the convex linear combination of $A(G)$ and $L(G)$ as $B_α(G) = αA(G) + (1-α)L(G)$, for $α\in [0,1]$. This paper presents some results on the eigenvalues of $B_α(G)$ and their multiplicity when some sets of vertices satisfy certain conditions. Moreover, the positive semidefiniteness problem of $B_α(G)$ is studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New results on $B_α$-eigenvalues of a graph Pastén, Germain Oliveira, Carla Silva Junior, João Domingos G. da Silva Justel, Claudia M. Discrete Mathematics 05C50, 05C05 Let $G$ be a graph with adjacency matrix $A(G)$ and Laplacian matrix $L(G)$. In 2024, Samanta \textit{et} \textit{al.} defined the convex linear combination of $A(G)$ and $L(G)$ as $B_α(G) = αA(G) + (1-α)L(G)$, for $α\in [0,1]$. This paper presents some results on the eigenvalues of $B_α(G)$ and their multiplicity when some sets of vertices satisfy certain conditions. Moreover, the positive semidefiniteness problem of $B_α(G)$ is studied. |
| title | New results on $B_α$-eigenvalues of a graph |
| topic | Discrete Mathematics 05C50, 05C05 |
| url | https://arxiv.org/abs/2510.16812 |