Designing an Aspect-Oriented Persistence Layer Supporting Object-Oriented Query Using the .NET Framework 3.5

In this article, we discuss aspect persistence, how it can be implemented in the .NET framework, and how to use the .NET framework to provide object-oriented queries for aspect-oriented persistence layers. The manner in which aspect-orientation can be available in the .NET framework is investigated in the first part of this article. Then the procedure through which adding persistence concepts to the .NET framework as aspects will be explained. In the next step, providing object-oriented querying is discussed, which is the main part of this article. Having object-oriented querying ability helps processes query in the same object-oriented domain in which objects are defined (not in the relation entities' domain). Language Integrated Query (LINQ) is used to provide the ability of querying in an object-oriented manner. Then, the translation of queries from the real objects' domain to the storage-objects' domain is explained. After such translation, the queries can be run by using the existing LINQ providers (for example LINQ to SQL). Finally, translating the result of queries back into the real objects' domain is discussed

Recursive Algorithms for Generation of Planar Graphs

In this thesis we introduce recursive algorithms for generation of two families of plane graphs. These algorithms start with small graphs and iteratively convert them to larger graphs. The families studied in this thesis are k-angulations (plane graphs with whose faces are of size k) and plane graphs with a given face size sequence.We also design a very fast method for canonical embedding and isomorphism rejection of plane graphs. Most graph generators like plantri generate graphs up to isomorphism of the embedding, however our method does the isomorphism checking up to the underlining graph while taking advantage of the planarity and embeddings to speed up the computation.The next subject discussed in this thesis is a type of graph called hypohamiltonian in which after removing each vertex from the graph, there is a Hamiltonian cycle through all remaining vertices while the original graph does not have any such cycle. One of the problems in the literature since 1976 is to find the smallest planar hypohamiltonian graphs. The previous record by Weiner and Araya was a planar graph with 42 vertices. We improve this record by finding 25 planar hypohamiltonian graphs on 40 vertices while discovering many larger ones on 42 and 43 vertices.The final subject in the thesis is a family of molecules called fullerenes which are entirely composed of carbon atoms. The structure of fullerenes are 3-connected plane graphs with exactly 12 faces of size 5 and the rest of size 6. A famous conjecture regarding fullerenes, called face-spiral conjecture claims that the drawing of their graph can be unwound in a spiral manner starting from one face and circulating around that face until all faces are traversed. This conjecture is known to be incorrect and the smallest counterexample is made of 380 carbon atoms. We have extended this conjecture to families of 3-connected plane graphs with f3, f4 and f5 faces of size 3, 4, and 5 while the remaining faces have size 6 and found counterexample for all possible values of . We also found the smallest counterexamples for 11 of these families out of 19 possible cases

Face-Spiral Codes in Cubic Polyhedral Graphs with Face Sizes no Larger Than 6

According to the face-spiral conjecture, first made in connection with enumeration of fullerenes, a cubic polyhedron can be reconstructed from a face sequence starting from the first face and adding faces sequentially in spiral fashion. This conjecture is known to be false, both for general cubic polyhedra and within the specific class of fullerenes. Here we report counterexamples to the spiral conjecture within the 19 classes of cubic polyhedra with positive curvature, i. e., with no face size larger than six. The classes are defined by triples {p3, p4, p5} where p3, p4 and p5 are the respective numbers of triangular, tetragonal and pentagonal faces. In this notation, fullerenes are the class {0, 0, 12}. For 11 classes, the reported examples have minimum vertex number, but for the remaining 8 classes the examples are not guaranteed to be minimal. For cubic graphs that also allow faces of size larger than 6, counterexamples are common and occur early; we conjecture that every infinite class of cubic polyhedra described by allowed and forbidden face sizes contains non-spiral elements

Face-spiral codes in cubic polyhedral graphs with face sizes no larger than 6

According to the face-spiral conjecture, first made in connection with enumeration of fullerenes, a cubic polyhedron can be reconstructed from a face sequence starting from the first face and adding faces sequentially in spiral fashion. This conjecture is known to be false, both for general cubic polyhedra and within the specific class of fullerenes. Here we report counterexamples to the spiral conjecture within the 19 classes of cubic polyhedra with positive curvature, i.e., with no face size larger than six. The classes are defined by triples {p (3), p (4), p (5)} where p (3), p (4) and p (5) are the respective numbers of triangular, tetragonal and pentagonal faces. In this notation, fullerenes are the class {0, 0, 12}. For 11 classes, the reported examples have minimum vertex number, but for the remaining 8 classes the examples are not guaranteed to be minimal. For cubic graphs that also allow faces of size larger than 6, counterexamples are common and occur early; we conjecture that every infinite class of cubic polyhedra described by allowed and forbidden face sizes contains non-spiral elements

Planar Hypohamiltonian Graphs on 40 Vertices

A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 42 vertices, a result due to Araya and Wiener. That result is here improved upon by 25 planar hypohamiltonian graphs of order 40, which are found through computer-aided generation of certain families of planar graphs with girth 4 and a fixed number of 4-faces. It is further shown that planar hypohamiltonian graphs exist for all orders greater than or equal to 42. If Hamiltonian cycles arereplaced by Hamiltonian paths throughout the definition of hypohamiltonian graphs, we get the definition of hypotraceable graphs. It is shown that there is a planar hypotraceable graph of order 154 and of all orders greater than or equal to 156. We also show that the smallest planar hypohamiltonian graph of girth 5 has 45 vertices.The first two authors were supported by the Australian Research Council. The work of the third author was supported in part by the Academy of Finland under the Grant Nos. 132122 and 289002; the work of the fourth author was supported by Grant No. 132122, the GETA Graduate School, and the Nokia Foundation. The last author is a PhD fellow at Ghent University on the BOF (Special Research Fund) scholarship 01DI1015