Introductory Map Theory by Yanpei Liu (PDF)

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As an introductory work, this book contains the elementary materials in map theory, includingembeddings of a graph, abstract maps, duality, orientable and non-orientable maps, isomorphisms of maps and the enumeration of rooted or unrooted maps, particularly, thejoint tree representation of an embedding of a graph on two dimensional manifolds, whichenables one to make the complication much simpler on map enumeration. All of theseare valuable for researchers and students in combinatorics, graphs and low dimensionaltopology.A Smarandache system (Sigma;R) is such a mathematical system with at leastone Smarandachely denied rule r in R such that it behaves in at least two different wayswithin the same set Sigma, i.e., validated and invalided, or only invalided but in multiple distinctways. A map is a 2-cell decomposition of surface, which can be seen as a connectedgraphs in development from partition to permutation, also a basis for constructing Smarandachesystems, particularly, Smarandache 2-manifolds for Smarandache geometries.

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