Protein and starch are important factors in determining wheat end-use quality and yield. However, these two traits are negatively correlated. So in order to dissect the genetic relationship between grain protein content (GPC) and grain starch content (GSC) at QTL/gene level, three mapping populations were used at three locations in 2 years. The QTLs for GPC and GSC were analyzed by unconditional and conditional QTL mappings. Thirteen QTLs were detected for GPC by each of the conditional and unconditional methods of QTL analyses. For GSC, seven and nine QTLs, respectively, were detected using unconditional and conditional QTL analyses methods. Of these QTLs, there was only one major QTL detected for GPC using unconditional QTL analysis. For GSC, two major QTLs were detected through each of the conditional and unconditional QTL mapping methods. Seven QTLs with minor effect on GSC were identified for GPC (Qgpc2A-12, Qgpc6D-3, Qgpc1D-15, Qgpc2D-23, Qgpc2D-31, Qgpc5B-19, and Qgpc4B-7). Four QTLs were found for GSC, named Qgsc1D-1, Qgsc4A-9, Qgsc7B-15, and Qgsc7D1-2, which had minor influence on GPC. The major QTL Qgsc7B-15 can directly be used for improving the GSC in molecular marker-assisted breeding. QTLs detected in the present study could possibly be used in simultaneous improvement of grain protein and starch content in wheat.

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The glutenin and waxy loci of wheat are important determinants of dough quality. This study was conducted to evaluate the effects of high-molecular-weight glutenin (HMW-GS) and waxy alleles on dough-mixing properties. Molecular mapping was used to investigate these effects on Mixograph properties in a population of 290 (Nuomai1 x Gaocheng8901) recombinant inbred lines (RILs) from three environments in the harvest years 2008, 2009 and 2011. The results indicated the following: (i) the Glu-A1 and Glu-D1 loci have greater impacts on Mixograph properties compared to the Wx-1 loci and the effects of Glu-D1d and Glu-D1h on dough mixing are better than those of Glu-D1f and Glu-D1new1 in this population; (ii) the interactions between the Glu-1 and Wx-1 loci affected some traits, especially the midline peak value (MPV), and the lack of Wx-B1 or Wx-D1 led to increased MPV for all types of Glu-1 loci; and (iii) 30 quantitative-trait loci (QTL) over nine wheat chromosomes were identified with ICIM analysis based on the genetic map of 498 loci. Eight major QTL and 16 QTL in the Glu-1 loci from the three environments were found. The major QTL clusters were associated with the Glu-1 loci, and also were found in two regions on chromosome 3B and one region on chromosome 6A, which is one of the novel chromosome regions influencing dough-mixing strength. The two QTL for MPV are located around Wx-B1 on chromosome 4A. QMPT-1D.1, QMPI-1D.1 and Q8MW-1D.1 were stable in different environments and could potentially be used in molecular marker-assisted breeding.

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Let Ln,t be the set of all n-vertex connected graphs with clique number t (2 ≤ t ≤ n). For nvertex connected graphs with given clique number, lexicographic ordering by spectral moments (S-order) is discussed in this paper. The first(n − t − 3i) + 1 graphs with 3 ≤ t ≤ n − 4, and the last few graphs, in the Sorder, among Ln,t are characterized. In addition, all graphs in Ln,n ∪ L n,n−1 have an S-order; for the cases t = n − 2 and t = n − 3, the first three and the first seven graphs in the set Ln,t are characterized, respectively. 2010 AMS Mathematics subject classification. Primary 05C50, 15A18. Keywords and phrases. Spectral moment, clique number, chromatic number.