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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

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Ordered algebraic structures --- Discrete mathematics --- Associative algebras --- Representations of algebras --- Representations of graphs --- Graphs, Representations of --- Graph theory --- Algebra --- Algebras, Associative --- Associative algebras. --- Representations of algebras. --- Representations of graphs. --- Algèbres associatives --- Représentations de graphes --- Représentations d'algèbres --- Algèbres associatives. --- Représentations de graphes. --- Représentations d'algèbres.

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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