Mo_8~ⅤW_2~ⅥO_(26)(C_5H_5N)_8·2H_2O: A Novel Mixed-valence Heterometal Polyoxometalate

A new mixed-valence heterometal cluster Mo8VW2VIO26(C5H5N)8·2H2O has been synthesized under solvothermal conditions and characterized by X-ray single-crystal diffraction, IR, UV-vis and XPS spectroscopy. The title compound crystallizes in the triclinic system, space group P1 with a = 11.708(3), b = 12.018(4), c = 13.316(4) , a = 112.184(4), β = 97.844(4), r = 110.043(3)o, V = 1551.9(8) 3 and Z = 1 at 293(2) K. The final full-matrix least-squares refinement converged to R = 0.0414 for 4460 observed unique reflections with I 2σ(I) and w R = 0.1290 for all data(5352) and S = 1.015. In addition, its thermal stability and fluorescent property have also been investigated.     

路的字典积的邻和可区别边染色

图G的正常[k]-边染色σ是指颜色集合为[k]={1,2,…,k}的G的一个正常边染色.用w_σ（x）表示顶点x关联边的颜色之和,即w_σ（x）=∑_e∋x σ（e）,并称w_σ（x）关于σ的权.图G的k-邻和可区别边染色是指相邻顶点具有不同权的正常[k]-边染色,最小的k值称为G的邻和可区别边色数,记为χ'_∑（G）.现得到了路P_n与简单连通图H的字典积P_n[H]的邻和可区别边色数的精确值,其中H分别为正则第一类图、路、完全图的补图.