Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (2): 23-31.

• Original Articles • Previous Articles     Next Articles

Some new families of Q-integral graphs

 WANG  Li-Gong1, CHEN  Yan-Qing1   

  1. 1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, 710072, China
  • Online:2012-06-15 Published:2012-06-15
  • Supported by:

    Supported by the National Natural Science Foundation of China (No.11171273), the Natural Science Foundation of Shaanxi Province (No.SJ08A01) and SRF for ROCS, SEM.

Abstract:  Let G be a simple graph. The matrix Q(G)=D(G)+A(G) denotes the signless Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix and the adjacency matrix of G respectively. A graph is called Q-integral if its signless Laplacian spectrum consists entirely of integers. In this paper, we firstly construct six infinite classes of nonregular Q-integral graphs from the known six smaller Q-integral graphs identified by Stani\'{c}.  Furthermore, we obtain large families of Q-integral graphs by  the Cartesian product of graphs. Finally, we obtain some regular Q-integral graphs.

Key words:  signless Laplacian spectrum, Q-integral graph, integral graph, integral eigenvalues