NOC:Advanced Graph Theory - Study24x7

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# NOC:Advanced Graph Theory

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In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically; see Graph (discrete mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

• Total 8 Modules
• 22 Videos
• Published on 29 June, 2019

## Week 01

• Paths, Cycles, and Trails

37m
• Eulerian Circuits, Vertex Degrees and Counting

37m
• Graph Theory: Introduction

37m

## Week 02

• Spanning Trees and Enumeration

46m
• Trees and Distance

46m
• The Chinese Postman Problem and Graphic Sequences

46m

## Week 03

• Matchings and Covers

1h 72 min
• Independent Sets, Covers and Maximum Bipartite Matching

1h 72 min
• Weighted Bipartite Matching

32m

## Week 04

• Factors & Perfect Matching in General Graphs

26m
• Stable Matchings and Faster Bipartite Matching

26m

## Week 05

• Connectivity and Paths: Cuts and Connectivity

1h 61 min
• k-Connected Graphs

1h 61 min
• Network Flow Problems

1h 61 min

## Week 06

• Vertex Coloring and Upper Bounds

44m
• Brook Theorem and Color-Critical Graphs

44m
• Counting Proper Colorings

44m

## Week 07

• Planar Graphs

28m
• Characterization of Planar Graphs

28m

## Week 08

• Line Graphs and Edge-coloring

1h 80 min
• Hamiltonian Graph, Traveling Salesman Problem and NP-Completeness

1h 80 min
• Connected Dominating Set and Distributed Algorithm

50m

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