Agave图类的无符号拉普拉斯谱半径的新改进界和Nordhaus-Gaddum型不等式

IF 1 Q1 MATHEMATICS
M. V., Kalyani Desikan
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引用次数: 0

摘要

核心-卫星图Θ(c, s, η) ~ = Kc△(ηKs)是由中心团Kc(核心)和k的η副本(卫星)在一个共同团中相遇组成的图。它们属于直径为2的图类。Agave图Θ(2,1, η) ~ = K2△(ηK1)属于完全分裂图的一般类型,其图由中心团K2和连接到团的所有节点的K1的η副本组成。它们是核心卫星图的子类。设μ(G)为无符号拉普拉斯矩阵Q(G)的谱半径。本文给出了Agave图的无符号拉普拉斯谱半径的最大下界和最小上界。这些边界用图不变量表示,如m(边数)、n(顶点数)、δ(最小度)、∆(最大度)和η个卫星副本。我们已经用了近似的方法来推导出这些边界。这种独特的方法可以用来确定任何一般图族的无符号拉普拉斯谱半径的边界。利用所导出的界,我们还得到了诺德豪斯-加达姆型不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New Improved Bounds for Signless Laplacian Spectral Radius and Nordhaus-Gaddum Type Inequalities for Agave Class of Graphs
Core-satellite graphs Θ(c, s, η) ∼= Kc ▽ (ηKs) are graphs consisting of a central clique Kc (the core) and η copies of Ks (the satellites) meeting in a common clique. They belong to the class of graphs of diameter two. Agave graphs Θ(2, 1, η) ∼= K2 ▽ (ηK1) belong to the general class of complete split graphs, where the graphs consist of a central clique K2 and η copies of K1 which are connected to all the nodes of the clique. They are the subclass of Core-satellite graphs. Let μ(G) be the spectral radius of the signless Laplacian matrix Q(G). In this paper, we have obtained the greatest lower bound and the least upper bound of signless Laplacian spectral radius of Agave graphs. These bounds have been expressed in terms of graph invariants like m the number of edges, n the number of vertices, δ the minimum degree, ∆ the maximum degree, and η copies of the satellite. We have made use of the approximation technique to derive these bounds. This unique approach can be utilized to determine the bounds for the signless Laplacian spectral radius of any general family of graphs. We have also obtained Nordhaus-Gaddum type inequality using the derived bounds.
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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