On the Spectrum of Laplacian Matrix

  title={On the Spectrum of Laplacian Matrix},
  author={Akbar Jahanbani and Seyed Mahmoud Sheikholeslami and R. Khoeilar},
  journal={Mathematical Problems in Engineering},
Let G be a simple graph of order n. +e matrixL(G) � D(G) − A(G) is called the Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let l1(G), ln− 1(G) be the largest eigenvalue, the second smallest eigenvalue of L(G) respectively, and λ1(G) be the largest eigenvalue of A(G). In this paper, we will present sharp upper and lower bounds for l1(G) and ln− 1(G). Moreover, we investigate the relation between l1(G) and λ1… 
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