Chapter 9 - Graph Theory

Section 9.0

9.0.1

Chapter

9

Graph Theory 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

9.1.1

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

CLASSROOM QUESTION


9.1.3

9.1.4


GRAPH-THEORETIC SOFTWARE


Section 9.2 Graph Terminology

9.2

GRAPH TERMINOLOGY DEGREE


9.2.1

9.2.2


CLASSROOM EXERCISE



SOCIOLOGICAL APPLICATIONS


9.2.3

9.2.4


GRAPH THEORETIC DEFINITIONS



SPECIAL GRAPHS


9.2.5

9.2.6





9.2.7

9.2.8


REGULAR GRAPHS

CLASSROOM EXERCISES



BIPARTITE GRAPHS


9.2.9

9.2.10


NEW GRAPHS FROM OLD


Section 9.3 Representations & Isomorphism

9.3.1

9.3 REPRESENTATIONS & ISOMORPHISM INCIDENCE TABLE REPRESENTATION


9.3.2


INCIDENCE MATRIX REPRESENTATION



9.3.3

ADJACENCY LIST REPRESENTATION

ADJACENCY MATRIX REPRESENTATION


9.3.4


GRAPH ISOMORPHISM




9.3.5

9.3.6


SIMPLE ISOMORPHISM




9.3.7

9.3.8


GRAPH ISOMORPHISM TESTING




9.3.9

9.3.10





9.3.11

Section 9.4 Connectivity

9.4

CONNECTIVITY WALKS and PATHS


9.4.1

9.4.2


SOME FINE POINTS OF WALKS




9.4.3

9.4.4


CYCLE GRAPHS and ISOMORPHISM




9.4.5

9.4.6


CONNECTEDNESS



NAIVE CONNECTEDNESS TEST


9.4.7

9.4.8


CUTPOINTS and CUTEDGES


Section 9.5 Euler and Hamilton Tours

9.5.1

9.5 EULER AND HAMILTON TOURS KÖNIGSBERG BRIDGE PROBLEM


9.5.2





9.5.3

9.5.4


HAMILTONIAN TOURS




9.5.5

9.5.6





9.5.7

Section 9.7 Planar Graphs

9.7

PLANAR GRAPHS

ORIENTABLE SURFACES


9.7.1

9.7.2


NONORIENTABLE SURFACES



SPHERE and PLANE


9.7.3

9.7.4


JORDAN CURVE THEOREM



KURATOWSKI GRAPHS


9.7.5

9.7.6


NONPLANARITY of



NONPLANARITY of


9.7.7

9.7.8





9.7.9

9.7.10





9.7.11

9.7.12





9.7.13

9.7.14


EDGE-FACE INEQUALITY




9.7.15

9.7.16




TWO NONPLANARITY CRITERIA


9.7.17

9.7.18



Section 9.8 Graph Coloring

9.8

GRAPH COLORING


9.8.1

9.8.2




OBSTRUCTIONS


9.8.3

9.8.4




APPLICATIONS


9.8.5

9.8.6


GREEDY COLORING ALGORITHM



MAP COLORING


9.8.7

9.8.8





9.8.9

9.8.10

