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

doi:10.1007/s11464-015-0452-4

Front. Math. China

2016, Vol. 11

Issue (3) : 623-645 https://doi.org/10.1007/s11464-015-0452-4

RESEARCH ARTICLE

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

Junjie YUE^1,²,Liping ZHANG^1,^*(

),Mei LU¹

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2. State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100910,China

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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 l≥3, 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 l≥5, 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 l≥5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.

Keywords H-eigenvalue hypergraph adjacency tensor signless Laplacian tensor Laplacian tensor loose path

Corresponding Author(s): Liping ZHANG

Issue Date: 17 May 2016

Cite this article:

Junjie YUE,Liping ZHANG,Mei LU. Largest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths[J]. Front. Math. China, 2016, 11(3): 623-645.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0452-4
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I3/623

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