Spectral radius and Average 2-Degree sequence of a Graph

@article{Huang2014SpectralRA,
  title={Spectral radius and Average 2-Degree sequence of a Graph},
  author={Yu-pei Huang and Chih-wen Weng},
  journal={Discrete Math., Alg. and Appl.},
  year={2014},
  volume={6}
}
Let G be a simple connected graph of order n with average 2degree sequence M1 ≥ M2 ≥ · · · ≥ Mn. Let ρ(G) denote the spectral radius of the adjacency matrix of G. We show that for each 1 ≤ l ≤ n and for any b ≥ max {di/dj | i ∼ j}, ρ(G) ≤ Ml − b+ √ (Ml + b)2 + 4b ∑l−1 i=1(Mi −Ml) 2 with equality if and only if M1 = M2 = · · · = Mn.