Complete characterization of odd factors via the size, spectral radius or distance spectral radius of graphs

Given a graph $G,$ a $\{1,3,\ldots,2n-1\}$-factor of $G$ is a spanning subgraph of $G$, in which each degree of vertices is one of $\{1,3,\ldots,2n-1\}$, where $n$ is a positive integer. In this paper, we first establish a lower bound on the size (resp.~the spectral radius) of $G$ to guarantee that...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2022, 59(4), , pp.1045-1067
Main Authors: Shuchao Li, Shujing Miao
Format: Article
Language:English
Subjects:
수학
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Summary:Given a graph $G,$ a $\{1,3,\ldots,2n-1\}$-factor of $G$ is a spanning subgraph of $G$, in which each degree of vertices is one of $\{1,3,\ldots,2n-1\}$, where $n$ is a positive integer. In this paper, we first establish a lower bound on the size (resp.~the spectral radius) of $G$ to guarantee that $G$ contains a $\{1,3,\ldots,2n-1\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{1,3,\ldots,2n-1\}$-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b210613