On the sum of k largest eigenvalues of graphs and symmetric matrices

  • Authors:

  • Bojan Mohar

  • Affiliations:

  • Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2009

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Abstract

Let k be a positive integer and let G be a graph of order n=k. It is proved that the sum of k largest eigenvalues of G is at most 12(k+1)n. This bound is shown to be best possible in the sense that for every k there exist graphs whose sum is 12(k+12)n-o(k^-^2^/^5)n. A generalization to arbitrary symmetric matrices is given.