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Machine theory --- Semirings (Mathematics) --- Formal languages --- 681.3*F4 --- Mathematical logic and formal languages (Theory of computation) --- 681.3*F4 Mathematical logic and formal languages (Theory of computation)

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The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version – the 'Traveling Salesman Problem' -, is still the subject of active research. Yet, it has been during the last fifty years or so—with the rise of the electronic computers—that Graph theory has become an indispensable discipline in terms of the number and importance of its applications across the Applied Sciences. Graph theory has been especially central to Theoretical and Algorithmic Computer Science, and Automatic Control, Systems Optimization, Economy and Operations Research, Data Analysis in the Engineering Sciences. Close connections between graphs and algebraic structures have been widely used in the analysis and implementation of efficient algorithms for many problems, for example: transportation network optimization, telecommunication network optimization and planning, optimization in scheduling and production systems, etc. The primary objectives of GRAPHS, DIOÏDS AND SEMIRINGS: New Models and Algorithms are to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties, while demonstrating the modeling and problem-solving capability and flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures, which either extend usual algebra (i.e., semirings), or correspond to a new branch of algebra (i.e., dioïds), apart from the classical structures of groups, rings, and fields.

Graph theory. --- Semirings (Mathematics) --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Rings (Algebra) --- Extremal problems --- Computer network architectures. --- Combinatorics. --- Operations research. --- Computational complexity. --- Operations Research, Management Science. --- Computer Systems Organization and Communication Networks. --- Operations Research/Decision Theory. --- Discrete Mathematics in Computer Science. --- Mathematical Modeling and Industrial Mathematics. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Combinatorics --- Algebra --- Mathematical analysis --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- Management science. --- Computer organization. --- Decision making. --- Computer science—Mathematics. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Organization, Computer --- Electronic digital computers --- Quantitative business analysis --- Operations research --- Statistical decision --- Decision making --- Computer engineering. --- Computer networks. --- Discrete mathematics. --- Operations Research, Management Science . --- Computer Engineering and Networks. --- Discrete Mathematics. --- Operations Research and Decision Theory. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Computers --- Distributed processing --- Design and construction