Download or read book Introductory Map Theory written by Yanpei Liu and published by Infinite Study. This book was released on 2010 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.