RESEARCH ARTICLE

Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths

  • Junjie YUE 1,2 ,
  • Liping ZHANG , 1 ,
  • Mei LU 1
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  • 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • 2. State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100910,China

Received date: 31 Oct 2014

Accepted date: 21 Jan 2015

Published date: 17 May 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We investigate k-uniform loose paths. We show that the largest Heigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l3, we show that the largest H-eigenvalue of its adjacency tensor is ((1+5)/2)2/k when l=3 and λ(A)=31/k when l=4, respectively. For the case of l5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval (2, 3) when l5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.

Cite this article

Junjie YUE , Liping ZHANG , Mei LU . Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 623 -645 . DOI: 10.1007/s11464-015-0452-4

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