On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

F. F. Wang; H. Y. Shan; Y. Y. Zhai

On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

Combinatorics 2021-06-18 v1

Authors: F. F. Wang , H. Y. Shan , Y. Y. Zhai

Abstract

The $\alpha$ -spectral radius of a connected graph $G$ is the spectral radius of $A_\alpha$ -matrix of $G$ . In this paper, we discuss the methods for comparing $\alpha$ -spectral radius of graphs. As applications, we characterize the graphs with the maximal $\alpha$ -spectral radius among all unicyclic and bicyclic graphs of order $n$ with diameter $d$ , respectively. Finally, we determine the unique graph with maximal signless Laplacian spectral radius among bicyclic graphs of order $n$ with diameter $d$ .

Keywords

spectral radius unicyclic graphs bicyclic graphs diameter a-alpha matrix signless laplacian

Cite

@article{arxiv.2106.09238,
  title  = {On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter},
  author = {F. F. Wang and H. Y. Shan and Y. Y. Zhai},
  journal= {arXiv preprint arXiv:2106.09238},
  year   = {2021}
}

On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

Abstract

Keywords

Cite

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