The Largest and Smallest Eigenvalues of Matrices and Some Hamiltonian Properties of Graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913560766971904 |
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| author | Li, Rao |
| author_facet | Li, Rao |
| contents | Let $G = (V, E)$ be a graph. We define matrices $M(G; α, β)$as $αD + βA$, where $α$, $β$ are real numbers such that $(α, β) \neq (0, 0)$ and $D$ and $A$ are the diagonal matrix and adjacency matrix of $G$, respectively. Using the largest and smallest eigenvalues of $M(G; α, β)$ with $α\geq β> 0$, we present sufficient conditions for the Hamiltonian and traceable graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Largest and Smallest Eigenvalues of Matrices and Some Hamiltonian Properties of Graphs Li, Rao Combinatorics Let $G = (V, E)$ be a graph. We define matrices $M(G; α, β)$as $αD + βA$, where $α$, $β$ are real numbers such that $(α, β) \neq (0, 0)$ and $D$ and $A$ are the diagonal matrix and adjacency matrix of $G$, respectively. Using the largest and smallest eigenvalues of $M(G; α, β)$ with $α\geq β> 0$, we present sufficient conditions for the Hamiltonian and traceable graphs. |
| title | The Largest and Smallest Eigenvalues of Matrices and Some Hamiltonian Properties of Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.17380 |