图的无符号拉普拉斯特征值α次幂总和的界

Bounds for the Sum of ath Powers of the Signless Laplacian Eigenvalues of Some Graphs

令G为简单图.sα（G）等于图G的无符号拉普拉斯特征值α次幂的总和,其中α为实数且α≠0,1.本文我们得到一些连通图的sα（G）的新的界,并给出了正则图的Mycielskian图、正则图及半正则二部图的Double图这些特殊图类的sα（G）的新的界.由这些结论的特殊情况可得到相应图的关联能量的界.

Let G be a simple graph. The graph invariant sa（G） is equal to the sum of ath powers of the signless Laplacian eigenvalues of G, for any real a（a ≠ 0,1）. In this paper, we obtain some new bounds for sα（G） of connected graphs. Moreover, we also give some new bounds for sα（G） of the Mycielskian of a regular graph and the Double graph of regular and semi-regular bipartite graphs. These results yield, as immediate special cases, bounds for the incidence energy.