Proof of a conjecture of V. Nikiforov


Using analytical tools, we prove that for any simple graph G on n vertices and its complement \(\bar G\) the inequality \(\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4} {3}n - 1\) holds, where μ(G) and \(\mu \left( {\bar G} \right)\) denote the greatest eigenvalue of adjacency matrix of the graphs G and \(\bar G\) respectively.

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Correspondence to Tamás Terpai.

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Supported by OTKA grant no. 81203.

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Terpai, T. Proof of a conjecture of V. Nikiforov. Combinatorica 31, 739–754 (2011).

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Mathematics Subject Classification (2000)

  • 05C35
  • 05C99