The graphs with the least distance eigenvalue at least

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• 作者：Dan Li ; Jixiang Meng ; ^{mjxxju@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：493
• 期：Complete
• 页码：358-380
• 全文大小：462 K

文摘

Let G be a connected graph with order n   and 5c578785128" title="Click to view the MathML source">D(G)$D(G)$ be the distance matrix of G  . Suppose that λ₁(D(G))≥⋯≥λ_n(D(G))${\lambda }_1(D(G))\ge \cdots \ge {\lambda }_n(D(G))$ are the distance spectra of G  . In this paper, we characterize the graphs with ${\lambda }_n(D(G))\in [-\frac{1+\sqrt{17}}{2},\alpha -1)\cup [\alpha -1,-1-\sqrt{2})$, where α   is the smallest root of x³−x²−3x+1=0$x^3-x^2-3x+1=0$, and $-\frac{1+\sqrt{17}}{2}<\alpha -1<-1-\sqrt{2}$. Furthermore, we show that the graphs with ${\lambda }_n\ge -\frac{1+\sqrt{17}}{2}$ are determined by their D-spectrum.