TY - JOUR

T1 - Asymptotic results on the spectral radius and the diameter of graphs

AU - Cioaba, S.M.

AU - van Dam, E.R.

AU - Koolen, J.H.

AU - Lee, J.H.

N1 - Appeared earlier as CentER DP 2008-71

PY - 2010

Y1 - 2010

N2 - We study graphswith spectral radius atmost 3/2√2 and refine results byWoo and Neumaier [R.Woo, A. Neumaier, On graphs whose spectral radius is bounded by 3/2√2, Graphs Combin. 23 (2007) 713–726]. We study the limit points of the spectral radii of certain families of graphs, and apply the results to the problem of minimizing the spectral radius among the graphs with a given number of vertices and diameter. In particular, we consider the cases when the diameter is about half the number of vertices, and when the diameter is near the number of vertices. We prove certain instances of a conjecture posed by Van Dam and Kooij [E.R. Van Dam, R.E. Kooij, The minimal spectral radius of graphs with a given diameter, Linear Algebra Appl. 423 (2007) 408–419] and show that the conjecture is false for the other instances.

AB - We study graphswith spectral radius atmost 3/2√2 and refine results byWoo and Neumaier [R.Woo, A. Neumaier, On graphs whose spectral radius is bounded by 3/2√2, Graphs Combin. 23 (2007) 713–726]. We study the limit points of the spectral radii of certain families of graphs, and apply the results to the problem of minimizing the spectral radius among the graphs with a given number of vertices and diameter. In particular, we consider the cases when the diameter is about half the number of vertices, and when the diameter is near the number of vertices. We prove certain instances of a conjecture posed by Van Dam and Kooij [E.R. Van Dam, R.E. Kooij, The minimal spectral radius of graphs with a given diameter, Linear Algebra Appl. 423 (2007) 408–419] and show that the conjecture is false for the other instances.

M3 - Article

VL - 432

SP - 722

EP - 737

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -