On the bounds of Laplacian eigenvalues of k-connected graphs
On the bounds of Laplacian eigenvalues of k-connected graphs
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DOI：
10.1007/s10587-015-0203-4
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发表时间：
2015-09
影响因子：
0.5
通讯作者：
Xiaodan Chen;Yaoping Hou
中科院分区：
文献类型：
--
作者：
Xiaodan Chen;Yaoping Hou
设µn−1(G)为代数连通度，µ1(G)为AK连通图的拉普拉斯谱半径。本文证明了当且仅当G是完全图KnorKn−e时，若G是非正则的，则{{(n(n-1)-2m)(n+k-2)+2{k^2}}$$是等价的。2增量--FRAC{{2(n\Delta-2m){k^2}}{{2(n\Delta-2m)({n^2}-2n+2k)+n{k^2}$，其中▵表示G的最大度。请注意，在某些情况下，这两个不等式改进了一些先前已知的结果。
Let µn−1(G) be the algebraic connectivity, and let µ1(G) be the Laplacian spectral radius of ak-connected graphGwithnvertices andmedges. In this paper, we prove that $${\mu _{n - 1}}(G) \geqslant \frac{{2n{k^2}}}{{(n(n - 1) - 2m)(n + k - 2) + 2{k^2}}}$$, with equality if and only ifGis the complete graphKnorKn−e. Moreover, ifGis non-regular, then $${\mu _1}(G) < 2\Delta - \frac{{2(n\Delta - 2m){k^2}}}{{2(n\Delta - 2m)({n^2} - 2n + 2k) + n{k^2}}}$$, where ▵ stands for the maximum degree ofG. Remark that in some cases, these two inequalities improve some previously known results.