Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16...Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the <em>k</em>-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.展开更多
To provide a theoretical basis for further improvement of Brassica napus yield, additive dominance with additive - by - additive epistatic effects （ ADAA） genetic model and a 6 X 8 partial dial- lel cross des...To provide a theoretical basis for further improvement of Brassica napus yield, additive dominance with additive - by - additive epistatic effects （ ADAA） genetic model and a 6 X 8 partial dial- lel cross design were used to analyze the genetic effects and correlations of five yield related traits of 14 excellent Brassica napus parental lines and their 46 and F2 populations. The results showed that silique density （SD） , siliques per plant （SPP） , seeds per silique （SPS） and thousand - seed weight （TSW） exhibited not only additive and dominant effects, but also significant epistatic effects. The dominant effects of all five yield - related traits were obviously greater than their additive effects and epistatic effects. Yield per plant （YPP） showed significant genetic correlation with SD, SPP and SPS, and the main component of the genetic correlation was the dominance correlation. SPP and SPS both showed a significant negative correlation with TSW. The SD of rapeseed was genetically correlated with all three components of yield to a certain extent, and there were different components of genetic effects positively correlated with the three yield components, indicating that SD is a potential trait to reconcile the conflict between TSW and SPP as well as SPS.展开更多
文摘Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the <em>k</em>-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.
基金This research was supported by the National Basic Research Program of China （ 973 Program, 2011CB109302）；the National High - Tech R＆D Pro-gram of China （863 Program, 2011AA10A104, 2012AA101107） ； Natural Science Foundation of Hu-bei Province （2015CFA103） ； Hubei Agricultural Science and Technology Innovation Center.
文摘To provide a theoretical basis for further improvement of Brassica napus yield, additive dominance with additive - by - additive epistatic effects （ ADAA） genetic model and a 6 X 8 partial dial- lel cross design were used to analyze the genetic effects and correlations of five yield related traits of 14 excellent Brassica napus parental lines and their 46 and F2 populations. The results showed that silique density （SD） , siliques per plant （SPP） , seeds per silique （SPS） and thousand - seed weight （TSW） exhibited not only additive and dominant effects, but also significant epistatic effects. The dominant effects of all five yield - related traits were obviously greater than their additive effects and epistatic effects. Yield per plant （YPP） showed significant genetic correlation with SD, SPP and SPS, and the main component of the genetic correlation was the dominance correlation. SPP and SPS both showed a significant negative correlation with TSW. The SD of rapeseed was genetically correlated with all three components of yield to a certain extent, and there were different components of genetic effects positively correlated with the three yield components, indicating that SD is a potential trait to reconcile the conflict between TSW and SPP as well as SPS.
