Gr aph Theor y - Columbia Universityabishek/files/DM-Ch9.pdf · Gr aph Theor y 9.1 Intr oduction to Graphs 9.2 Graph T erminology 9.3 Represention and Isomorphism 9.4 Connectivity

Section 9.0 9.0.1

Chapter 9GraphTheory

9.1 Introduction to Graphs

9.2 Graph Terminology

9.3 Represention and Isomorphism

9.4 Connectivity

9.5 Euler and Hamilton Paths

9.6* Shortest Path Problems

9.7 Planar Graphs

9.8 Graph Coloring

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 9.1 Introduction to Graphs 9.1.1

9.1 INTRODUCTION TO GRAPHS

Fig 9.1.1


9.1.2 Chapter 9 Graph Theory

Fig 9.1.2

OPTIONAL FEATURES of GRAPHS

Fig 9.1.3


Section 9.1 Introduction to Graphs 9.1.3

CLASSROOM QUESTION



GRAPH-THEORETIC SOFTWARE


Section 9.2 Graph Terminology 9.2.1

9.2 GRAPH TERMINOLOGY

DEGREE



CLASSROOM EXERCISE



SOCIOLOGICAL APPLICATIONS



GRAPH THEORETIC DEFINITIONS



SPECIAL GRAPHS







REGULAR GRAPHS

CLASSROOM EXERCISES



BIPARTITE GRAPHS



NEW GRAPHS FROM OLD


Section 9.3 Representations & Isomorphism 9.3.1

9.3 REPRESENTATIONS & ISOMORPHISM

INCIDENCE TABLE REPRESENTATION



INCIDENCE MATRIX REPRESENTATION



ADJACENCY LIST REPRESENTATION

ADJACENCY MATRIX REPRESENTATION



GRAPH ISOMORPHISM





SIMPLE ISOMORPHISM





GRAPH ISOMORPHISM TESTING








Section 9.4 Connectivity 9.4.1

9.4 CONNECTIVITY

WALKS and PATHS



SOME FINE POINTS OF WALKS





CYCLE GRAPHS and ISOMORPHISM





CONNECTEDNESS



NAIVE CONNECTEDNESS TEST



CUTPOINTS and CUTEDGES


Section 9.5 Euler and Hamilton Tours 9.5.1

9.5 EULER AND HAMILTON TOURS

KÖNIGSBERG BRIDGE PROBLEM







HAMILTONIAN TOURS








Section 9.7 Planar Graphs 9.7.1

9.7 PLANAR GRAPHS

ORIENTABLE SURFACES



NONORIENTABLE SURFACES



SPHERE and PLANE



JORDAN CURVE THEOREM



KURATOWSKI GRAPHS



NONPLANARITY of



NONPLANARITY of















EDGE-FACE INEQUALITY







TWO NONPLANARITY CRITERIA




Section 9.8 Graph Coloring 9.8.1

9.8 GRAPH COLORING





OBSTRUCTIONS





APPLICATIONS



GREEDY COLORING ALGORITHM



MAP COLORING








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Gr aph Theor y - Columbia Universityabishek/files/DM-Ch9.pdf · Gr aph Theor y 9.1 Intr oduction to Graphs 9.2 Graph T erminology 9.3 Represention and Isomorphism 9.4 Connectivity