a b s t r a c tThis paper introduces the concept of the fractional Thue chromatic number of graphs and studies the relation between the fractional Thue chromatic number and the Thue chromatic number. We determine the fractional Thue chromatic number of all paths, all trees with no vertices of degree two, and all cycles, except C 10 , C 14 , C 17 . As a consequence, we prove that if G is a path or a tree with no degree two vertices, then its fractional Thue chromatic number equals its Thue chromatic number. On the other hand, we show that there are trees and cycles whose fractional Thue chromatic numbers are strictly less than their Thue chromatic numbers.

1,1′-Bichrysene-2,2′-diol and its thiophene analogs, 6,6′-biphenanthro-[1,2- b]thiophene-7,7′-diols, as a series of novel π-expanded chrysene-/phenanthro[1,2- b]thiophene-based axially chiral molecules are synthesized from 1,1′-bi-2-naphthols with key steps including a Suzuki coupling, a Wittig reaction, and acid-mediated cyclization.

A stereoselective synthesis of C1-b-dxylopyranoside derivatives had been developed via intramolecular 1,3-acyloxy migration/Ferrier rearrangement stategy from readily available propargylic carboxylates and d-xylal. A combined catalytic system of chloro(triphenylphosphine)gold(I) (Ph 3 PAuCl) and silver hexafluoroantimonate (AgSbF 6 ) was found to possess the most effective of the reaction, and 20 examples tested the wide functional compatibility for these transformation. Nuclear magnetic resonance (NMR), infrared spectrum (IR), high resolution electrospray ionization mass spectroscopy (HRESIMS) and isotopic labelling experiments were utilized to investigate the C1-glycosylation process. The relative configuration for the products was determined by two-dimensional (2D) NMR NMR and electronic circular dichroism spectroscopy. 3-(4,5)-Dimethylthiahiazo (-z-y1)-3,5-diphenytetrazoliumro-mide (MTT) cell viability assays indicated that three of them showed strong anti-proliferative activities against human gastric cancer HGC-27 cells with IC 50 values of 17.09-38.88 mM. This method opened up new horizons for the synthesis of bioactive C-glycosylated molecules.

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