A lower bound for the spectral radius of graphs with fixed diameter

  • Authors:

  • Sebastian M. Cioab;Edwin R. van Dam;Jack H. Koolen;Jae-Ho Lee

  • Affiliations:

  • Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;Department of Econometrics and O.R., Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;Department of Mathematics, Pohang University of Science and Technology, Hyoja-dong, Namgu, Pohang 790-784, Republic of Korea;Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706-1388, USA

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2010

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Abstract

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.