Year: 2025
Type: preprint
Abstract: The $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor of a graph is a spanning subgraph whose each component is an element of $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a $\{K_2\}$-factor. We get a lower bound on the size (resp. the spectral radius) of $G$ to guarantee that $G$ contains a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{K_{1,1}, K_{1,2},C_m: m\geq3\}$-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.
Source: arXiv (Cornell University)
Authors: Ren, Fengyun, Zhang, Shumin, Wang, Ke
Institutions: Qinghai Normal University, Beijing Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6372693338, G7471968010
OpenAlex ID: W4407123541