Spectral Characterizations of Some Distance-Regular Graphs

When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2,1), (3,1) and (4,1), the Biggs-Smith graph, the M ₂₂ graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.     

Tm3+/Yb3+共掺铋碲酸盐玻璃中的高效蓝色上转换荧光

制备了高折射率Tm3+/Yb3+共掺杂铋碲酸盐玻璃,利用棱镜耦合法测量出玻璃在632.8和1550 nm波长处的折射率分别为2.0365和1.9795. 对玻璃的吸收、荧光和红外透过光谱展开了测试与分析,根据Judd-Ofelt理论对吸收光谱进行拟合,求得Tm3+的振子强度参数Ωt(t=2,4,6)分别为3.90×10-20, 2.03×10-20和9.03×10-21 cm2,并进一步计算了Tm3+在玻璃中各能级跃迁的振子强度、自发辐射跃迁概率、辐射寿命和荧光分支比等光谱参数. 在980 nm激光激发下测得强的蓝色三光子上转换和近红外双光子上转换荧光. 宽的红外透过窗口、高的折射率和强的蓝色上转换荧光表明,Tm3+/Yb3+共掺铋碲酸盐玻璃有希望成为高效的上转换发光和激光材料.     

Distance-regular Cayley graphs with least eigenvalue $$$$

We classify the distance-regular Cayley graphs with least eigenvalue \(-2\) and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular Cayley line graphs of incidence graphs of generalized polygons.