Matching, odd $[1,b]$-factor and distance spectral radius of graphs with given some parameters
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909940592934912 |
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| author | Xu, Zengzhao Xi, Weige Wang, Ligong |
| author_facet | Xu, Zengzhao Xi, Weige Wang, Ligong |
| contents | For a connected graph $G$, let $μ(G)$ denote the distance spectral radius of $G$. A matching in a graph $G$ is a set of disjoint edges of $G$. The maximum size of a matching in $G$ is called the matching number of $G$, denoted by $α(G)$. An odd $[1, b]$-factor of a graph $G$ is a spanning subgraph $G_0$ such that the degree $d_{G_0}(v)$ of $v$ in $G_0$ is odd and $1\le d_{G_0}(v)\le b$ for every vertex $v\in V (G)$. In this paper, we give a sharp upper bound in terms of the distance spectral radius to guarantee $α(G)>\frac{n-k}{2}$ in an $n$-vertex $t$-connected graph $G$, where $2\le k \le n-2$ is an integer. We also present a sharp upper bound in terms of distance spectral radius for the existence of an odd $[1,b]$-factor in a graph with given minimum degree $δ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matching, odd $[1,b]$-factor and distance spectral radius of graphs with given some parameters Xu, Zengzhao Xi, Weige Wang, Ligong Combinatorics For a connected graph $G$, let $μ(G)$ denote the distance spectral radius of $G$. A matching in a graph $G$ is a set of disjoint edges of $G$. The maximum size of a matching in $G$ is called the matching number of $G$, denoted by $α(G)$. An odd $[1, b]$-factor of a graph $G$ is a spanning subgraph $G_0$ such that the degree $d_{G_0}(v)$ of $v$ in $G_0$ is odd and $1\le d_{G_0}(v)\le b$ for every vertex $v\in V (G)$. In this paper, we give a sharp upper bound in terms of the distance spectral radius to guarantee $α(G)>\frac{n-k}{2}$ in an $n$-vertex $t$-connected graph $G$, where $2\le k \le n-2$ is an integer. We also present a sharp upper bound in terms of distance spectral radius for the existence of an odd $[1,b]$-factor in a graph with given minimum degree $δ$. |
| title | Matching, odd $[1,b]$-factor and distance spectral radius of graphs with given some parameters |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.14433 |