论文信息 - On a conjecture of V. Nikiforov

On a conjecture of V. Nikiforov

In this paper we will prove that @m(G)[email protected]([email protected]?)@?1+32n-1. where @m(G),@m([email protected]?) are the greatest eigenvalues of the adjacency matrices of the graph G and its complement and n denotes the number of vertices of G.

Péter Csikvári

[1] Vladimir Nikiforov,et al. Linear combinations of graph eigenvalues , 2006, math/0608198.

[2] Vladimir Nikiforov. Eigenvalue problems of Nordhaus-Gaddum type , 2007, Discret. Math..

[3] Charles J. Colbourn,et al. Network transformations and bounding network reliability , 1993, Networks.

[4] A. Kelmans. On graphs with randomly deleted edges , 1981 .

[5] Peter Rowlinson. On the maximal index of graphs with a prescribed number of edges , 1988 .

[6] Appajosyula Satyanarayana,et al. A reliability-improving graph transformation with applications to network reliability , 1992, Networks.

[7] A. Hoffman,et al. On the spectral radius of (0,1)-matrices , 1985 .