Book Description:
Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus to study problems in geometry. Graph theory is also a growing area in mathematical research. In mathematics and computer science, graph theory is the study of mathematical structures used to model pairwise relations between objects from a certain collection. This book presents various theories and applications in both of these mathematical fields. Included are the concepts of dominating sets, one of the most widely studied concepts in graph theory, some current developments of graph theory in the fields of planar linkage mechanisms and geared linkage mechanisms, lie algebras and the application of CR Hamiltonian flows to the deformation theory of CR structures.

Table of Contents:
Preface

Chapter 1. Applications of Graph Theory in Mechanism Analysis, pp. 1-34
(T.J. Li, School of Electromechanical Engineering, Xidian Univ., Shaanxi Province, Xi'an, China, W.Q. Cao, Dept. of Mechanical Engineering, Xi'an Univ. of Technology, Shaanxi Province, Xi'an, China, T.H. Yan, R & D Center, Shanghai Micro-Electronics Equipment Co., Ltd., Shanghai, China)

Chapter 2. A Categorical Perspective on Connections with Application in the Formulation of Functorial Physical Dynamics, pp. 35-77
(Elias Zafiris, Univ. of Athens, Dept. of Mathematics, Athens, Greece)

Chapter 3. The Notion of CR Hamiltonian Flows and the Local Embedding Problem of CR Structures, pp. 79-94
(Takao Akahori, Department of Mathematics, School of Science, University of Hyogo, Himeji, Hyogo)

Chapter 4. Equivariant Methods in Combinatorial Geometry, pp. 95-133
(Pavle V.M. Blagojevic, Serbian Ministry of Science, Technology and Development, Serbia)

Chapter 5. Something New About Reconstruction, pp. 135-186
(Elena Konstantinova, Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia)

Chapter 6. Coalescence of Graphs, pp. 187-222
(A.A. Lushnikov, Karpov Institute of Physical Chemistry, Moscow, Russia)

Chapter 7. Graph Analysis with Application to Economics, pp. 223-297
(Andre A. Keller, Faculté de Sciences Economiques, Sociales et Juridiques, Université de Haute Alsace, Mulhouse, France)

Chapter 8. Application of Hilbert spaces to the Stability Study of flows on A Sphere, pp. 299-344
(Yuri N. Skiba, Universidad Nacional Autonoma de Mexico)

Chapter 9. A Functorial Approach to the Infinitesimal Theory of Groupoid, pp. 345-372
(Hirokazu Nishimura, Institute of Mathematics, Univ. of Tsukuba, Tsukuba, Ibaraki, Japan)

Chapter 10. A Model of Higher-Order Concurrent Programs Based on Graph Rewriting, pp. 373-394
(Masaki Murakami, Dept. of Computer Science, Graduate School of Natural Science and Technology, Okayama Univ., Tsushima-Naka, Okayama, Japan)

Chapter 11. Protecting the Vertices of A Graph, pp. 395-409
(William F. Klostermeyer, School of Computing, Univ. of North Florida, Jacksonville, FL)

Index