Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs

Emina I. Milovanovic; Igor Z. Milovanovic

Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs

Spectral Theory 2015-06-19 v1

Authors: Emina I. Milovanovic , Igor Z. Milovanovic

Abstract

Let $G$ be a connected undirected graph with $n$ , $n\ge 3$ , vertices and $m$ edges. Denote by $\rho_1 \ge \rho_2 \ge \cdots > \rho_n =0$ the normalized Laplacian eigenvalues of $G$ . Upper and lower bounds of $\rho_i$ , $i=1,2,\ldots , n-1$ , are determined in terms of $n$ and general Randi\' c index, $R_{-1}$ .

Keywords

normalized Laplacian eigenvalue graph upper bound lower bound Randić index spectral graph theory

Cite

@article{arxiv.1506.05762,
  title  = {Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs},
  author = {Emina I. Milovanovic and Igor Z. Milovanovic},
  journal= {arXiv preprint arXiv:1506.05762},
  year   = {2015}
}

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