PPT-Chapter 6: Graphs 6.2 The Euler Characteristic

Chapter 6 Graphs 62 The Euler Characteristic Draw A Graph Any connected graph you want but dont make it too simple or too crazy complicated Only rule No edges can cross unless theres a vertex where theyre crossing. We solve the problem of counting the total number of observab le targets eg persons vehicles landmarks in a region using local counts perform ed by a network of sensors each of which measures the number of targets nearby but neither their identiti GRAPHS gah Agraphon4nodes gbh Adirectedgraphon4nodes qigureYSWeTwographseMaNanundirectedgraphQandMbNadirectedgraphS willbeundirectedunlessnotedotherwiseS GraphsasModelsofNetworksw rraphsareusefulbecausetheyserveasmathematical modelsofnetworkstructure N. etworks and Graphs. Euler Paths and Circuits. Can You draw this figure without lifting you pencil from the paper?. The original problem. . A resident of Konigsberg wrote to Leonard Euler saying that a popular pastime for couples was to try to cross each of the seven beautiful bridges in the city exactly once -- without crossing any bridge more than once.. . 1707-1784 . Leonhard Euler was born in Basel, but the family moved to . Riehen. when he was one year old and it was in . Riehen. , not far from Basel, that Leonard was brought up. Paul Euler, his father, had some mathematical training and he was able to teach his son elementary mathematics along with other subjects.. Graphs. Fall . 2011. Sukumar Ghosh. Seven Bridges of . K. ⍥. nigsberg. Is it possible to walk along a route that cross . each bridge exactly once?. Seven Bridges of . K. ⍥. nigsberg. A Graph. What is a Graph. When an Euler path is impossible, we can get an approximate path. In the approximate path, some edges will need to be retraced. An . optimal approximation. of a Euler path is a path with the minimum number of edge . = number of vertices – number of edges + number of faces. Or in short-hand,. . . = |V| - |E| + |F|. where V = set of vertices. E = set of edges. F = set of faces. of a series of preparatory lectures for the Fall 2013 online course MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology. Target Audience: Anyone interested in . 24-28 October 2016. 11. Graphs and Trees 1. . Graphs: Definitions. . Trails, Paths, and Circuits Matrix Representations Isomorphisms. 1. . . Graphs: Definitions . Trails, Paths, and Circuits Matrix Representations Isomorphisms. Lesson Plan. Euler Circuits. Parking-Control . Officer Problem. Finding Euler Circuits. Qualifications: Even Valence and Connectedness. Beyond Euler Circuits. Chinese Postman Problem. Eulerizing. a Graph. Chapter 10. Chapter Summary. Graphs and Graph Models. Graph Terminology and Special Types of Graphs. Representing Graphs and Graph Isomorphism. Connectivity. Euler and Hamiltonian Graphs. Shortest-Path Problems (. Graphs and Graph Models. Graph Terminology and Special Types of Graphs. Representing Graphs and Graph Isomorphism. Connectivity. Euler and Hamiltonian Paths. Graphs and Graph Models. Section . 10.1. Section Summary. 1. Learning Objectives:. Know how to use graphs as models and how to determine efficient paths.. Modeling with graphs. Euler circuits. Degrees of vertices and Euler’s Theorem. Chapter . 7 Graph Theory. Exercise 8.2. Isomorphic Graphs. Graphs with same number of vertices edges & the same number of connections between vertices. If vertices labelled same way, matrix representation will be the same.