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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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This volume is an outcome of the International conference held in Tata Institute of Fundamental Research and the University of Hyderabad. There are fifteen articles in this volume. The main purpose of the articles is to introduce recent and advanced techniques in the area of analytic and algebraic geometry. This volume attempts to give recent developments in the area to target mainly young researchers who are new to this area. Also, some research articles have been added to give examples of how to use these techniques to prove new results.

Mathematics. --- Algebraic geometry. --- Associative rings. --- Rings (Algebra). --- Commutative algebra. --- Commutative rings. --- Functions of complex variables. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Associative Rings and Algebras. --- Several Complex Variables and Analytic Spaces. --- Geometry, algebraic. --- Algebra. --- Differential equations, partial. --- Partial differential equations --- Mathematics --- Mathematical analysis --- Algebraic geometry --- Geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Algebra --- Associative algebras. --- Algebras, Associative --- Geometry, Algebraic.