一個2 ( , ,)v k λ − 設計 ， ()|k m nK Kλ 對應 於 Group Divisible Design (可分組

英文摘要： The main focus of the study of graph-design is to decompose a graph H into isomorphic copies of subgraphs G, denoted by G|H. It is well-known that |k vK Kλ is equivalent to the existence of a 2 ( , ,)v k λ− design and ()|k m nK Kλ is equivalent to the existence of a group divisible design [ , ; ,]GD n m k λ. Therefore, the study of combinatorial designs plays an important role in our study. The use of combinatorial designs in experiment designs has been known for many occasions. Thus, we intend to add more which are related to modern technologies. Also, we expect to find more other types of designs such as grid-block design. Note that this design has its application on DNA Library Screening (related to DNA sequencing). Besides, we also utilize the packing of graph to obtain well-constructed SONET and better disjunct matrices which are the main objectives in nonadaptive algorithms of group testing