# Search results for: Xueliang Li

Discrete Mathematics > 2008 > 308 > 24 > 6383-6391

Discrete Mathematics > 2004 > 283 > 1-3 > 231-241

Applied Mathematics-A Journal of Chinese Universities > 2004 > 19 > 1 > 17-26

Discrete Mathematics > 2008 > 308 > 24 > 6383-6391

A graph is called integral if all its eigenvalues (of the adjacency matrix) are integers. In this paper, the graphs K1,r•Kn, r∗Kn, K1,r•Km,n, r∗Km,n and the tree K1,s•T(q,r,m,t) are defined. We determine the characteristic polynomials of these graphs and also obtain sufficient and necessary conditions for these graphs to be integral. Some sufficient conditions are found by using the number theory...

Discrete Mathematics > 2004 > 283 > 1-3 > 231-241

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantine equations...

Applied Mathematics-A Journal of Chinese Universities > 2004 > 19 > 1 > 17-26

In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.