当前位置: X-MOL 学术Linear Multilinear Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Note on distance signless Laplacian spectral radius under given matching number
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-04-27 , DOI: 10.1080/03081087.2020.1756200
Yan Liu 1 , Jin Yan 1
Affiliation  

ABSTRACT

Let n,β be the family of graphs with n vertices and with the matching number β. The distance signless Laplacian spectral radius of a graph G is denoted by ρ(G). Li and Sun (Matching number, connectivity and eigenvalues of distance signless Laplacians. Linear Multilinear Algebra, 2019. https://doi.org/10.1080/03081087.2019.1588218) proved that if n72β, ρ(G)ρ(KβKnβ¯) for any Gn,β, with equality if and only if G=KβKnβ¯. Further Li and Sun conjectured that if 2β+2n72β, the statement holds. In this paper, we disprove this conjecture by an example, when n = 19 and β=8. Further by using a different technique, we show that the statement holds for n258β.



中文翻译:

给定匹配数下距离无符号拉普拉斯光谱半径的注意事项

摘要

n,β是具有n个顶点和匹配数β的图族。图G的距离无符号拉普拉斯谱半径表示为ρ(G). Li 和 Sun(Matching number, connectivity and eigenvalues of distanceless Laplacians. Linear Multilinear Algebra, 2019. https://doi.org/10.1080/03081087.2019.1588218)证明如果n72β,ρ(G)ρ(ķβķn-β¯)对于任何Gn,β, 相等当且仅当G=ķβķn-β¯. Li 和 Sun 进一步推测,如果2β+2n72β,该陈述成立。在本文中,我们通过一个例子来反驳这个猜想,当n  = 19 并且β=8. 进一步通过使用不同的技术,我们证明该陈述适用于n258β.

更新日期:2020-04-27
down
wechat
bug