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E-raamat: Basic Graph Theory

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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.

Preface.- Graphs and Their Applications.- Basic Graph Terminologies.- Paths, Cycles and Connectivity"s.- Trees.- Matching and Covering.- Planar Graphs.- Graph Coloring.- Digraphs.- Special Classes of Graphs.- Some Research Topics.- Index.

Arvustused

The content is presented in a simple and straightforward manner with ample illustrations using neat and apt diagrams (graphs). The book is definitely good for students learning graph theory at the undergraduate and postgraduate levels. (Sudev Naduvath, Computing Reviews, January, 9 , 2018)

1 Graphs and Their Applications
1(10)
1.1 Introduction
1(1)
1.2 Applications of Graphs
2(9)
1.2.1 Map Coloring
2(1)
1.2.2 Frequency Assignment
3(1)
1.2.3 Supply Gas to a Locality
4(2)
1.2.4 Floorplanning
6(1)
1.2.5 Web Communities
7(1)
1.2.6 Bioinformatics
7(1)
1.2.7 Software Engineering
8(1)
Exercises
8(1)
References
9(2)
2 Basic Graph Terminologies
11(20)
2.1 Graphs and Multigraphs
11(2)
2.2 Adjacency, Incidence, and Degree
13(2)
2.2.1 Maximum and Minimum Degree
13(1)
2.2.2 Regular Graphs
14(1)
2.3 Subgraphs
15(1)
2.4 Some Important Trivial Classes of Graphs
16(3)
2.4.1 Null Graphs
17(1)
2.4.2 Complete Graphs
17(1)
2.4.3 Independent Set and Bipartite Graphs
17(1)
2.4.4 Path Graphs
18(1)
2.4.5 Cycle Graphs
19(1)
2.4.6 Wheel Graphs
19(1)
2.5 Operations on Graphs
19(3)
2.5.1 Union and Intersection of Graphs
19(1)
2.5.2 Complement of a Graph
20(1)
2.5.3 Subdivisions
21(1)
2.5.4 Contraction of an Edge
22(1)
2.6 Graph Isomorphism
22(2)
2.7 Degree Sequence
24(2)
2.8 Data Structures and Graph Representation
26(5)
2.8.1 Adjacency Matrix
26(1)
2.8.2 Incidence Matrix
27(1)
2.8.3 Adjacency List
28(1)
Exercises
28(1)
References
29(2)
3 Paths, Cycles, and Connectivity
31(16)
3.1 Walks, Trails, Paths, and Cycles
31(3)
3.2 Eulerian Graphs
34(2)
3.3 Hamiltonian Graphs
36(3)
3.4 Connectivity
39(8)
3.4.1 Connected Separable Graphs
41(1)
3.4.2 Block-Cutvertex Tree
42(1)
3.4.3 2-Connected Graphs
43(1)
3.4.4 Ear Decomposition
44(2)
Exercises
46(1)
References
46(1)
4 Trees
47(16)
4.1 Introduction
47(1)
4.2 Properties of a Tree
47(3)
4.3 Rooted Trees
50(1)
4.4 Spanning Trees of a Graph
51(3)
4.5 Counting of Trees
54(4)
4.6 Distances in Trees and Graphs
58(1)
4.7 Graceful Labeling
59(4)
Exercises
60(2)
References
62(1)
5 Matching and Covering
63(14)
5.1 Matching
63(5)
5.1.1 Perfect Matching
63(1)
5.1.2 Maximum Matching
63(3)
5.1.3 Hall's Matching Condition
66(2)
5.2 Independent Set
68(1)
5.3 Covers
68(1)
5.4 Dominating Set
69(3)
5.5 Factor of a Graph
72(5)
Exercises
73(1)
References
74(3)
6 Planar Graphs
77(14)
6.1 Introduction
77(1)
6.2 Characterization of Planar Graphs
77(1)
6.3 Plane Graphs
78(7)
6.3.1 Euler's Formula
82(2)
6.3.2 Dual Graph
84(1)
6.4 Thickness of Graphs
85(1)
6.5 Straight-Line Drawings of Planar Graphs
85(6)
Exercises
89(1)
References
89(2)
7 Graph Coloring
91(12)
7.1 Introduction
91(1)
7.2 Vertex Coloring
91(3)
7.3 Edge Coloring
94(3)
7.4 Face Coloring (Map Coloring)
97(1)
7.5 Chromatic Polynomials
97(1)
7.6 Acyclic Coloring
98(5)
Exercises
101(1)
References
102(1)
8 Digraphs
103(8)
8.1 Introduction
103(1)
8.2 Digraph Terminologies
103(2)
8.3 Eulerian Digraphs
105(1)
8.4 Hamiltonian Digraphs
106(1)
8.5 Digraphs and Tournaments
106(1)
8.6 Flow Networks
107(4)
Exercises
109(1)
References
109(2)
9 Special Classes of Graphs
111(24)
9.1 Introduction
111(1)
9.2 Outerplanar Graphs
111(3)
9.3 Triangulated Plane Graphs
114(7)
9.3.1 Canonical Ordering
114(2)
9.3.2 Separating Triangles
116(3)
9.3.3 Plane 3-Trees
119(2)
9.4 Chordal Graphs
121(3)
9.5 Interval Graphs
124(1)
9.6 Series-Parallel Graphs
125(5)
9.7 Tree width and Pathwidth
130(5)
Exercises
131(1)
References
132(3)
10 Some Research Topics
135(30)
10.1 Introduction
135(1)
10.2 Graph Representation
135(2)
10.3 Graph Drawing
137(11)
10.3.1 Drawings of Planar Graphs
138(7)
10.3.2 Simultaneous Embedding
145(1)
10.3.3 Drawings of Nonplanar Graphs
146(2)
10.4 Graph Labeling
148(2)
10.5 Graph Partitioning
150(2)
10.6 Graphs in Bioinformatics
152(4)
10.6.1 Hamiltonian Path for DNA Sequencing
152(1)
10.6.2 Cliques for Protein Structure Analysis
153(1)
10.6.3 Pairwise Compitability Graphs
154(2)
10.7 Graphs in Wireless Sensor Networks
156(9)
10.7.1 Topology Control
157(1)
10.7.2 Fault Tolerance
158(1)
10.7.3 Clustering
158(1)
References
159(6)
Index 165
Md. Saidur Rahman is a Professor in the Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET). He has taught basic graph theory at undergraduate level for more than ten years. Professor Rahman specialized in theoretical computer science and researches on algorithms, graph theory, graph drawing, computational geometry and bioinformatics. Prof. Rahman is a Fellow of Bangladesh Academy of Sciences and a Senior Member of IEEE.
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