Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The Structural Representation of Proximity Matrices with MATLAB presents and demonstrates the use of functions within a MATLAB computational environment, affecting various structural representations for the proximity information that is assumed to be available on a set of objects. The representations included in the book have been developed primarily in the behavioral sciences and applied statistical literature, although interest in these topics now extends more widely to such fields as bioinformatics and chemometrics. This book is divided into three main sections, each based on the general class of representations being discussed. Part I develops linear and circular unidimensional and multidimensional scaling using the city-block metric as the major representational device. Part II discusses characterizations based on various graph-theoretic tree structures, specifically those referred to as ultrametrics and additive trees. Part III uses representations defined solely by order properties, particularly emphasizing what are called (strongly) anti-Robinson forms.

Functions. --- Proximity matrices. --- Representations of graphs. --- MATLAB.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author's original work on graph embeddings, this book is an essential reference for researchers in graph theory. ContentsAbstract GraphsAbstract MapsDualityOrientabilityOrientable MapsNonorientable MapsIsomorphisms of MapsAsymmetrizationAsymmetrized Petal BundlesAsymmetrized MapsMaps within SymmetryGenus PolynomialsCensus with PartitionsEquations with PartitionsUpper Maps of a GraphGenera of a GraphIsogemial GraphsSurface Embeddability

Representations of graphs. --- Representations of algebras. --- Associative algebras. --- Algebras, Associative --- Algebra --- Graphs, Representations of --- Graph theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Conceptual structures (Information theory) --- Representations of graphs --- Reasoning --- Computer simulation --- Argumentation --- Ratiocination --- Reason --- Thought and thinking --- Judgment (Logic) --- Logic --- Graphs, Representations of --- Graph theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

539.19 --- Physics of single molecules --- Chemistry, Physical and theoretical. --- Configuration space. --- Many-body problem. --- Quantum theory. --- Representations of graphs. --- 539.19 Physics of single molecules --- Many-body problem --- Quantum theory --- Chemistry, Physical and theoretical --- Configuration space --- Representations of graphs --- Problème des N corps --- Théorie quantique --- Chimie physique et théorique --- Représentations de graphes

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is the first comprehensive introduction to the theory of word-representable graphs, a generalization of several classical classes of graphs, and a new topic in discrete mathematics. After extensive introductory chapters that explain the context and consolidate the state of the art in this field, including a chapter on hereditary classes of graphs, the authors suggest a variety of problems and directions for further research, and they discuss interrelations of words and graphs in the literature by means other than word-representability. The book is self-contained, and is suitable for both reference and learning, with many chapters containing exercises and solutions to seleced problems. It will be valuable for researchers and graduate and advanced undergraduate students in discrete mathematics and theoretical computer science, in particular those engaged with graph theory and combinatorics, and also for specialists in algebra. .

Computer Science --- Engineering & Applied Sciences --- Graph theory. --- Representations of graphs. --- Graphs, Representations of --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Computer science. --- Computers. --- Computer science --- Algebra. --- Computer Science. --- Theory of Computation. --- Mathematics of Computing. --- Mathematics. --- Combinatorial analysis --- Topology --- Information theory. --- Mathematics --- Mathematical analysis --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Computer science—Mathematics. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Computer mathematics --- Electronic data processing