# Search results for: Xueliang Li

Linear Algebra and its Applications > 2016 > 497 > C > 199-208

Complexity > 21 > 1 > 35 - 41

Discrete Applied Mathematics > 2007 > 155 > 10 > 1254-1266

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

Linear Algebra and its Applications > 2016 > 497 > C > 199-208

The energy E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. If a graph G of order n has the same energy as the complete graph Kn, i.e., if E(G)=2(n−1), then G is said to be borderenergetic. We obtain three asymptotically tight bounds on the edge number of borderenergetic graphs. Then, by using disconnected regular graphs we construct connected...

Complexity > 21 > 1 > 35 - 41

Dehmer and Mowshowitz introduced a class of generalized graph entropies using known information‐theoretic measures. These measures rely on assigning a probability distribution to a graph. In this article, we prove some extremal properties of such generalized graph entropies by using the graph energy and the spectral moments. Moreover, we study the relationships between the generalized graph entropies...

Discrete Applied Mathematics > 2007 > 155 > 10 > 1254-1266

A graph G is called integral if all eigenvalues of its adjacency matrix A(G) are integers. In this paper, the trees T(p,q)•T(r,m,t) and K1,s•T(p,q)•T(r,m,t) of diameter 6 are defined. We determine their characteristic polynomials. We also obtain for the first time sufficient and conditions for them to be integral. To do so, we use number theory and apply a computer search. New families of integral...

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...