publication . Preprint . 2011

Diameters of Graphs with Spectral Radius at most $3/2\sqrt{2}$

Lan, Jingfen; Lu, Linyuan;
Open Access English
  • Published: 21 Dec 2011
The spectral radius $\rho(G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix. Woo and Neumaier discovered that a connected graph $G$ with $\rho(G)\leq 3/2{\sqrt{2}}$ is either a dagger, an open quipu, or a closed quipu. The reverse statement is not true. Many open quipus and closed quipus have spectral radius greater than $3/2{\sqrt{2}}$. In this paper we proved the following results. For any open quipu $G$ on $n$ vertices ($n\geq 6$) with spectral radius less than $3/2{\sqrt{2}}$, its diameter $D(G)$ satisfies $D(G)\geq (2n-4)/3$. This bound is tight. For any closed quipu $G$ on $n$ vertices ($n\geq 13$) with spectral radius less than $3/2{\sq...
free text keywords: Mathematics - Combinatorics, 05C50, 05C35
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NSF| Extremal and Probabilistic Combinatorics II
  • Funder: National Science Foundation (NSF)
  • Project Code: 1000475
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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