On the spectral radius of graphs without a star forest

Let F=∪i=1kSdi be the union of pairwise vertex-disjoint k stars of order d1+1,…,dk+1, respectively, where k≥2 and d1≥⋯≥dk≥1. In this paper, we present two sharp upper bounds for the spectral radius of F-free (bipartite) graphs and characterize all corresponding extremal graphs. Moreover, the minimum...

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Bibliographic Details
Published inDiscrete mathematics Vol. 344; no. 4; p. 112269
Main Authors Chen, Ming-Zhu, Liu, A-Ming, Zhang, Xiao-Dong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2021
Subjects
Bipartite graph
Extremal graph
Spectral radius
Star forest
Star forest
Bipartite graph
Spectral radius
Extremal graph
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Summary:Let F=∪i=1kSdi be the union of pairwise vertex-disjoint k stars of order d1+1,…,dk+1, respectively, where k≥2 and d1≥⋯≥dk≥1. In this paper, we present two sharp upper bounds for the spectral radius of F-free (bipartite) graphs and characterize all corresponding extremal graphs. Moreover, the minimum least eigenvalue of the adjacency matrix of an F-free graph and all extremal graphs are obtained.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.112269