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INTRODUCTORY MAP THEORY

book
Language:
Author: YANPEI LIU
Url: http://fs.gallup.unm.edu//MapTheory.pdf
Format: Pdf
Year: 2010
Category: Graph Theory
Pages: 503
Clicks: 114

Description
This book contains the following chapters in company with related subjects. In Chapter I, the embedding of a graph on surfaces are much concerned because they are motivated to building up the theo ry of abstract maps related with Smarandache geometry. The second chapter is for the formal definition of abstract maps. One can see that this matter is a natural generalization of gr aph embedding on surfaces. The third chapter is on the duality not only for maps themselves but also for operations on maps from one surface to another. One can see how the duality is naturally deduced from the abstract maps described in the second chapter. The fourth chapter is on the orientability. One can see how the orientability is formally designed as a combinatorial invariant. The fifth chapter concentrates on the classification of orientable maps. The sixth chapter is for the classification of nonorientable maps. From the two chapters: Chapter V and Chapter VI, one can see how the procedure is simplified for these classifications. The seventh chapter is on the isomorphisms of maps and pro- vides an efficient algorithm for the justification and recogni tion of the isomorphism of two maps, which has been shown to be useful for determining the automorphism group of a map in the eighth chapter. Moreover, it enables us to access an automorphism of a graph. The ninth and the tenth chapters observe the number of distinct asymmetric maps with the size as a parameter. In the former, only one vertex maps are counted by favorite formulas and in the latter, general maps are counted from differential equations. . The next chapter, Chapter XI, only presents some ideas for accessing the symmetric census of maps and further, of graphs. This topic is being developed in some other directions and left as a subject written in the near future. From Chapter XII through Chapter XV, extensions from basic theory are much concerned with further applications. Chapter XII discusses in brief on genus polynomial of a graph and all its super maps rooted and unrooted on the basis of the joint tree model. Recent progresses on this aspect are referred to read the articles.

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