NPTEL Syllabus
Graph Theory - Web course
COURSE OUTLINE
Preliminaries: Graphs,isomorphism, subgraphs, matrix
representations, degree, operations on graphs, degree
sequences
Connected graphs and shortest paths: Walks, trails,
paths, connected graphs, distance, cut-vertices, cut-edges,
blocks, connectivity, weighted graphs, shortest path
algorithms
Trees: Characterizations, number of trees, minimum
spanning trees
Special classes of graphs: Bipartite graphs, line graphs,
chordal graphs
NPTEL
http://nptel.iitm.ac.in
Mathematics
Eulerian graphs: Characterization, Fleury’s algorithm,
chinese-postman-problem
Hamilton graphs: Necessary conditions and sufficient
conditions
Independent sets, coverings, matchings: Basic
equations, matchings in bipartite graphs, perfect matchings,
greedy and approximation algorithms
Vertex colorings: Chromatic number and cliques, greedy
coloring algorithm, coloring of chordal graphs, Brook’s
theorem
Edge colorings: Gupta-Vizing theorem, Class-1 graphs
and class-2 graphs, equitable edge-coloring
Planar graphs: Basic concepts, Eulers formula,
polyhedrons and planar graphs, charactrizations, planarity
testing, 5-color-theorem
Directed graphs: Out-degree, in-degree, connectivity,
orientation, Eulerian directed graphs, Hamilton directed
graphs, tournaments
COURSE DETAIL
Modules
Contents (optional
topics are indicated
in bold)
Number
of
lectures
Number
of
lectures
Additional Reading:
1. F.Harary: Graph
Theory, Narosa,
(1988)
2. C. Berge: Graphs
and Hypergraphs,
North
Holland/Elsevier,
(1973)
Coordinators:
Prof. S.A. Choudum
Department of
MathematicsIIT Madras
by
skipping
optional
topics
1.
Preliminaries
Graphs,
isomorphism,
subgraphs, matrix
representations,
degree, operations
on graphs, degree
sequences
5-10
4
2. Connected
graphs and
shortest
paths
Walks, trails, paths,
connected graphs,
distance, cut-vertices,
cut-edges, blocks,
weighted graphs,
connectivity,
Dijkstra’s shortest
path algorithm,
Floyd-Warshall
shortest path
algorithm
4-8
4
3. Trees
Characterizations,
number of trees,
minimum spanning
trees
5-10
4
4. Special
classes of
graphs
Bipartite graphs, line
graphs, chordal
graphs
6-12
2
5. Eulerian
graphs
Characterization,
Fleury’s algorithm,
chinese-postmanproblem
2-4
2
6. Hamilton
graphs
Necessary conditions
and sufficient
conditions
4-8
4
7.
Independent
sets,
Basic equations,
matchings in bipartite
graphs, perfect
8-16
6
coverings
and
mathcings
matchings, greedy
and approximation
algorithms
8. Vertexcolorings
Chromatic number
and cliques, greedy
coloring algorithm,
coloring of chordal
graphs, Brook’s
theorem
4-8
2
9. Edgecolorings
Gupta-Vizing
theorem, Class-1
graphs and class-2
graphs, equitable
edge-coloring
8-16
6
10. Planar
graphs
Basic concepts,
Eulers formula,
polyhedrons and
planar graphs,
charactrizations,
planarity testing, 5color-theorem
10-20
3
11. Directed
graphs
Directed graph,
underlying graph, outdegree, in-degree,
connectivity,
orientation, Eulerian
directed graphs,
Hamilton directed
graphs,
tournaments
8-16
6
References:
Text Books:
1. J.A. Bondy and U.S.R.Murty: Graph Theory and Applications (
Freely downloadable from Bondy's website; Google-Bondy)
2. D.B.West: Introduction to Graph Theory, Prentice-Hall of
India/Pearson, 2009 ( latest impression)
Reference Books:
1. J.A.Bondy and U.S.R.Murty: Graph Theory, Springer, 2008.
2. R.Diestel: Graph Theory, Springer( low price edition) 2000.
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http://nptel.iitm.ac.in