An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

NASA SBIR abstracts of 1990 phase 1 projects

The research objectives of the 280 projects placed under contract in the National Aeronautics and Space Administration (NASA) 1990 Small Business Innovation Research (SBIR) Phase 1 program are described. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses in response to NASA's 1990 SBIR Phase 1 Program Solicitation. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 280, in order of its appearance in the body of the report. The document also includes Appendixes to provide additional information about the SBIR program and permit cross-reference in the 1990 Phase 1 projects by company name, location by state, principal investigator, NASA field center responsible for management of each project, and NASA contract number

Generation of Graph Classes with Efficient Isomorph Rejection

In this thesis, efficient isomorph-free generation of graph classes with the method of generation by canonical construction path(GCCP) is discussed. The method GCCP has been invented by McKay in the 1980s. It is a general method to recursively generate combinatorial objects avoiding isomorphic copies. In the introduction chapter, the method of GCCP is discussed and is compared to other well-known methods of generation. The generation of the class of quartic graphs is used as an example to explain this method. Quartic graphs are simple regular graphs of degree four. The programs, we developed based on GCCP, generate quartic graphs with 18 vertices more than two times as efficiently as the well-known software GENREG does. This thesis also demonstrates how the class of principal graph pairs can be generated exhaustively in an efficient way using the method of GCCP. The definition and importance of principal graph pairs come from the theory of subfactors where each subfactor can be modelled as a principal graph pair. The theory of subfactors has applications in the theory of von Neumann algebras, operator algebras, quantum algebras and Knot theory as well as in design of quantum computers. While it was initially expected that the classification at index 3 + √5 would be very complicated, using GCCP to exhaustively generate principal graph pairs was critical in completing the classification of small index subfactors to index 5¼. The other set of classes of graphs considered in this thesis contains graphs without a given set of cycles. For a given set of graphs, H, the Turán Number of H, ex(n,H), is defined to be the maximum number of edges in a graph on n vertices without a subgraph isomorphic to any graph in H. Denote by EX(n,H), the set of all extremal graphs with respect to n and H, i.e., graphs with n vertices, ex(n,H) edges and no subgraph isomorphic to any graph in H. We consider this problem when H is a set of cycles. New results for ex(n, C) and EX(n, C) are introduced using a set of algorithms based on the method of GCCP. Let K be an arbitrary subset of {C3, C4, C5, . . . , C32}. For given n and a set of cycles, C, these algorithms can be used to calculate ex(n, C) and extremal graphs in Ex(n, C) by recursively extending smaller graphs without any cycle in C where C = K or C = {C3, C5, C7, . . .} ᴜ K and n≤64. These results are considerably in excess of the previous results of the many researchers who worked on similar problems. In the last chapter, a new class of canonical relabellings for graphs, hierarchical canonical labelling, is introduced in which if the vertices of a graph, G, is canonically labelled by {1, . . . , n}, then G\{n} is also canonically labelled. An efficient hierarchical canonical labelling is presented and the application of this labelling in generation of combinatorial objects is discussed

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control

The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Large space structures and systems in the space station era: A bibliography with indexes (supplement 05)

Bibliographies and abstracts are listed for 1363 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1991 and July 31, 1992. Topics covered include technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion and solar power satellite systems