Remoteness and distance eigenvalues of a graph
Remoteness and distance eigenvalues of a graph
复制标题
图的距离和距离特征值
DOI：
10.1016/j.dam.2016.07.018
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发表时间：
2016-12-31
影响因子：
1.1
通讯作者：
Wu, Baoyindureng
中科院分区：
文献类型：
--
作者：
Lin, Huiqiu;Das, Kinkar Ch.;Wu, Baoyindureng
设G是直径为d的n阶连通图，G的距离Rho是一个顶点到所有其他顶点的最大平均距离，偏导数(1)>；=…>；=偏导数(N)是G.Aouchiche和Hansen(0000)的距离特征值，Aouchiche和Hansen猜想，当d>；=3时，Rho+偏导数(左垂直7d/右垂直)>；0时，Rho+偏导数(3)>；0.在本文中，我们证实了这两个猜想。此外，我们还给出了当G与K-n不同余时偏导数(N)+Rho和偏导数(1)-Rho的下界，并刻画了极图。(C)2016爱思唯尔B.V.保留所有权利。
Let G be a connected graph of order n with diameter d. Remoteness rho of G is the maximum average distance from a vertex to all others and partial derivative(1) >= ... >= partial derivative(n) are the distance eigenvalues of G. Aouchiche and Hansen (0000), Aouchiche and Hansen conjectured that rho + partial derivative(3) > 0 when d >= 3 and rho + partial derivative(left perpendicular7d//right perpendicular) > 0. In this paper, we confirm these two conjectures. Furthermore, we give lower bounds on partial derivative(n) + rho and partial derivative(1) - rho when G not congruent to K-n and the extremal graphs are characterized. (C) 2016 Elsevier B.V. All rights reserved.