几类特殊图的拉普拉斯Estrada指标估计

应用回归分析法得到路和格子图的Laplacian Extrada index估计式;应用积分逼近原理得到圈及其补图、轮图的Laplacian Extrada index估计式;讨论了单点粘合图的Laplacian Estrada指标问题,给出了单点粘合图G·G的LEE的上界和下界.

关于边控制集的一些结论

令 G=(V,E)是一个图 ,M是边集 E(G)的子集 .如果有 e∈E(G) /M,e至少与 M中一条边相连 ,则称 M为图 G的边控制集 .进一步 ,若 M是匹配 ,则称 M为图 G独立边控制集 .本文给出关于边控制集的一些结论 .(1 )设图 H,S是两个连通图 .且 H,S∈ Ж,γe(S) =1 ,M和 M′={uv}分别是图 H和 S的唯一最小边控制集 ,其中 S是图 1中的 (G1 ,G2 ,G3,G4 )四个图之一 .对任何点 x∈V(S) -{u,v},y∈V(H) -V(M) .令 G=H(y=x) S,则 G∈Ж.(2 )如果连通图 G≠K2 ,G∈ Ж,γe(G) =k,则存在 G的两个连通子图 H,S和某两个正整数 l,m使 H∈ Ж,S∈Ж,且 γe(H) =k-l,γe(S) =l,G≌H(yi=xi) S,其中 l i m.

Effect of Viscosities on Mixing in A Patterned Micro Mixer

The effect of viscosity and viscosity difference and boundary patterned slip on mixing in a micro mixer has been numerically studied using lattice Boltzmann method （LBM）. The slip and no-slip ratio is not constant and varies irregularly, and viscosity is altered by changing the relaxation time in LBE equation. The slip boundary condition is simulated by specular reflection boundary and the no-slip boundary condition is simulated by bounce back boundary. It has been found that it is feasible to optimize the micro mixer design by combining the viscosity effect and boundary patterned ratio altogether.