The spanning k-trees, perfect matchings and spectral radius of graphs

A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we gi...

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Published inLinear & multilinear algebra Vol. 70; no. 21; pp. 7264 - 7275
Main Authors Fan, Dandan, Goryainov, Sergey, Huang, Xueyi, Lin, Huiqiu
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 20.12.2022
Taylor & Francis Ltd
Subjects
Graph theory
k-tree
perfect matching
spectral radius
Trees (mathematics)
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Summary:A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we provide a sufficient condition for the existence of a k-tree in a connected graph with fixed order in terms of the adjacency spectral radius and the signless Laplacian spectral radius, respectively. Also, we give a similar condition for the existence of a perfect matching in a balanced bipartite graph with fixed order and minimum degree.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2021.1985055