Basic Graph Theory 1st Edition by Md Saidur Rahman ISBN 3319494740 978-3319494746

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Product details:

ISBN 10: 3319494740 

ISBN 13: 978-3319494746

Author: Md. Saidur Rahman

This undergraduate textbook provides an introduction to graph theory, which has numerous applications in modeling problems in science and technology, and has become a vital component to computer science, computer science and engineering, and mathematics curricula of universities all over the world.

The author follows a methodical and easy to understand approach. Beginning with the historical background, motivation and applications of graph theory, the author first explains basic graph theoretic terminologies. From this firm foundation, the author goes on to present paths, cycles, connectivity, trees, matchings, coverings, planar graphs, graph coloring and digraphs as well as some special classes of graphs together with some research topics for advanced study.

Filled with exercises and illustrations, Basic Graph Theory is a valuable resource for any undergraduate student to understand and gain confidence in graph theory and its applications to scientific research, algorithms and problem solving.

Table of contents: 

1. Graphs and Their Applications

1.1 Introduction

1.2 Applications of Graphs

1.2.1 Map Coloring

1.2.2 Frequency Assignment

1.2.3 Supply Gas to a Locality

1.2.4 Floorplanning

1.2.5 Web Communities

1.2.6 Bioinformatics

1.2.7 Software Engineering

2. Basic Graph Terminologies

2.1 Graphs and Multigraphs

2.2 Adjacency, Incidence, and Degree

2.2.1 Maximum and Minimum Degree

2.2.2 Regular Graphs

2.3 Subgraphs

2.4 Some Important Trivial Classes of Graphs

2.4.1 Null Graphs

2.4.2 Complete Graphs

2.4.3 Independent Set and Bipartite Graphs

2.4.4 Path Graphs

2.4.5 Cycle Graphs

2.4.6 Wheel Graphs

2.5 Operations on Graphs

2.5.1 Union and Intersection of Graphs

2.5.2 Complement of a Graph

2.5.3 Subdivisions

2.5.4 Contraction of an Edge

2.6 Graph Isomorphism

2.7 Degree Sequence

2.8 Data Structures and Graph Representation

2.8.1 Adjacency Matrix

2.8.2 Incidence Matrix

2.8.3 Adjacency List

3. Paths, Cycles, and Connectivity

3.1 Walks, Trails, Paths, and Cycles

3.2 Eulerian Graphs

3.3 Hamiltonian Graphs

3.4 Connectivity

3.4.1 Connected Separable Graphs

3.4.2 Block-Cutvertex Tree

3.4.3 2-Connected Graphs

3.4.4 Ear Decomposition

4. Trees

4.1 Introduction

4.2 Properties of a Tree

4.3 Rooted Trees

4.4 Spanning Trees of a Graph

4.5 Counting of Trees

4.6 Distances in Trees and Graphs

4.7 Graceful Labeling

5. Matching and Covering

5.1 Matching

5.1.1 Perfect Matching

5.1.2 Maximum Matching

5.1.3 Hall’s Matching Condition

5.2 Independent Set

5.3 Covers

5.4 Dominating Set

5.5 Factor of a Graph

6. Planar Graphs

6.1 Introduction

6.2 Characterization of Planar Graphs

6.3 Plane Graphs

6.3.1 Euler’s Formula

6.3.2 Dual Graph

6.4 Thickness of Graphs

6.5 Straight-Line Drawings of Planar Graphs

7. Graph Coloring

7.1 Introduction

7.2 Vertex Coloring

7.3 Edge Coloring

7.4 Face Coloring (Map Coloring)

7.5 Chromatic Polynomials

7.6 Acyclic Coloring

8. Digraphs

8.1 Introduction

8.2 Digraph Terminologies

8.3 Eulerian Digraphs

8.4 Hamiltonian Digraphs

8.5 Digraphs and Tournaments

8.6 Flow Networks

9. Special Classes of Graphs

9.1 Introduction

9.2 Outerplanar Graphs

9.3 Triangulated Plane Graphs

9.3.1 Canonical Ordering

9.3.2 Separating Triangles

9.3.3 Plane 3-Trees

9.4 Chordal Graphs

9.5 Interval Graphs

9.6 Series-Parallel Graphs

9.7 Treewidth and Pathwidth

10. Some Research Topics

10.1 Introduction

10.2 Graph Representation

10.3 Graph Drawing

10.3.1 Drawings of Planar Graphs

10.3.2 Simultaneous Embedding

10.3.3 Drawings of Nonplanar Graphs

10.4 Graph Labeling

10.5 Graph Partitioning

10.6 Graphs in Bioinformatics

10.6.1 Hamiltonian Path for DNA Sequencing

10.6.2 Cliques for Protein Structure Analysis

10.6.3 Pairwise Compatibility Graphs

10.7 Graphs in Wireless Sensor Networks

10.7.1 Topology Control

10.7.2 Fault Tolerance

10.7.3 Clustering

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Md Saidur Rahman,Basic Graph Theory