On the Spectrum of Laplacian Matrix

Akbar Jahanbani, Seyed Mahmoud Sheikholeslami and Rana Khoeilar

Mathematical Problems in Engineering, 2021, vol. 2021, 1-4

Abstract:

Let be a simple graph of order . The matrix is called the Laplacian matrix of , where and denote the diagonal matrix of vertex degrees and the adjacency matrix of , respectively. Let , be the largest eigenvalue, the second smallest eigenvalue of respectively, and be the largest eigenvalue of . In this paper, we will present sharp upper and lower bounds for and . Moreover, we investigate the relation between and .

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8096874

DOI: 10.1155/2021/8096874

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