Spanning k-trees and distance spectral radius in graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913435886813184 |
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| author | Zhou, Sizhong Wu, Jiancheng |
| author_facet | Zhou, Sizhong Wu, Jiancheng |
| contents | Let $k\geq2$ be an integer. A tree $T$ is called a $k$-tree if $d_T(v)\leq k$ for each $v\in V(T)$, that is, the maximum degree of a $k$-tree is at most $k$. Let $λ_1(D(G))$ denote the distance spectral radius in $G$, where $D(G)$ denotes the distance matrix of $G$. In this paper, we verify a upper bound for $λ_1(D(G))$ in a connected graph $G$ to guarantee the existence of a spanning $k$-tree in $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08846 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spanning k-trees and distance spectral radius in graphs Zhou, Sizhong Wu, Jiancheng Combinatorics 05C50, 05C05, 05C70 Let $k\geq2$ be an integer. A tree $T$ is called a $k$-tree if $d_T(v)\leq k$ for each $v\in V(T)$, that is, the maximum degree of a $k$-tree is at most $k$. Let $λ_1(D(G))$ denote the distance spectral radius in $G$, where $D(G)$ denotes the distance matrix of $G$. In this paper, we verify a upper bound for $λ_1(D(G))$ in a connected graph $G$ to guarantee the existence of a spanning $k$-tree in $G$. |
| title | Spanning k-trees and distance spectral radius in graphs |
| topic | Combinatorics 05C50, 05C05, 05C70 |
| url | https://arxiv.org/abs/2304.08846 |