Some Results on the Principal Eigenvector

WU Chun-jie

doi:10.13371/j.cnki.chin.q.j.m.2020.04.008

Chinese Quarterly Journal of Mathematics >

2020 , Vol. 35 >Issue 4: 401 - 409

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2020.04.008

Some Results on the Principal Eigenvector

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School of Minsheng College, Henan University, Kaifeng 475004, China

WU Chunjie (1988-), male, native of Jiaozuo, Henan, lecture of Henan University Minsheng College, engages in graph theory.

Received date: 2020-06-30

Online published: 2021-01-06

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Abstract

For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G) (resp. Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G) (resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.

Key words： ; Signless Laplacian; Principal eigenvector; Independent set; k-Regular; Semiregular

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WU Chun-jie . Some Results on the Principal Eigenvector[J]. Chinese Quarterly Journal of Mathematics, 2020 , 35(4) : 401 -409 . DOI: 10.13371/j.cnki.chin.q.j.m.2020.04.008

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