一些特殊图类乘积的离散度

连通图的离散度是用s(G)来表示的,s(G)=max{ω(G-S)-|S|:ω(G-S)>1,SV(G)}.给出了两个完全图乘积的和一个完全图与路的乘积的离散度.还给出了两个完全图乘积的坚韧度.     

图的字典积的非零整数流(英文)

充分利用图的字典积的结构证明了以下结论:如果图G_1的每连通分支都非平凡,图G_2的阶数大于3,那么它们的字典积G_1[G_2]具有非零3-流.     

Biological assays and theoretical density functional theory calculations of Rh(I), Ir(III), and Ru(II) complexes of chiral phosphinite ligand

Four metal complexes, IL-OPPh₂-Ru-p-cymene (3) , IL-OPPh₂-Ru-benzene (4) , IL-OPPh₂-Ir-Cp* (5) , IL-OPPh₂-Rh-COD (6) , have been evaluated for in vitro antioxidant activity such as 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging and reducing power activity. Maximum scavenging activity (71.43%) was obtained with IL-OPPh₂-Ru-p-cymene, whereas IL-OPPh₂-Rh-COD showed the highest reducing power ability. The complexes were also studied for their antimicrobial activity against three Gram-positive and three Gram-negative bacteria. In addition, DNA binding of the complexes was evaluated using calf thymus DNA. Both Ru(II) complexes exhibited good DNA-binding activity while the other complexes did not have any activity. Furthermore, ab initio quantum calculations of four complexes were also carried out using density functional theory to better understand their chemical behaviors.     

一类2连通（n,n＋2）图的色类

本文研究了围长为6的K_4同胚图的色性,对于其中的非色唯一图,给出了其色类。     

COMPARISION THEOREMS OF THE TOPOLOGICAL PROPERTIES FOR A NEW MODEL OF ISOMERS

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Enumeration of 2-regular circulant graphs and directed double networks

We present a formula to enumerate non-isomorphic circulant digraphs of order n with connection sets of cardinality 2. This formula simplifies to C(n,2)=3×2^a−1−4 in the case when n=2^a(a≥3), and when n=p^a(where p is an odd prime and a≥1). The number of non-isomorphic directed double networks are also enumerated.     

The effect of light and dye composition on the color of dyeings with indigo, 6-bromoindigo,and 6,6′-dibromoindigo,components of Tyrian purple

Quantitative HPLC and colorimetry are used to study color variations in dyeings with indigo, 6-bromoindigo, and 6,6′-dibromoindigo, the main components of the historic dye Tyrian purple. For the first time, visible light is identified conclusively as a cause of debromination of the leuco form of 6-bromoindigo. A dyeing run using 6-bromoindigo alone is found to yield a dyed fabric containing large amounts of indigo, when the vat is exposed to visible light. The extent of debromination is dependent upon the pH of the dye bath and also the source of the visible light. This information allowed development of a dyeing procedure which is demonstrated to give consistent colors through two passes. Quantitative HPLC analysis of extracts from the dyed fabrics indicates that the leuco form of 6-bromoindigo vs. the leuco forms of indigo and 6,6′-dibromoindigo has the strongest affinity for wool fabric. This is postulated to be due to attractive electrostatic interactions between the leuco form of 6-bromoindigo and wool.

     

Nowhere‐zero flows in tensor product of graphs

In this paper, we characterize graphs whose tensor product admit nowhere‐zero 3‐flow. The main result is: For two graphs G₁ and G₂ with δ ≥ 2 and G₂ not belonging to a well‐characterized class of graphs, the tensor product of G₁ and G₂ admits a nowhere‐zero 3‐flow. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 284–292, 2007