Graphs and Networks. S. R. Kingan

Graphs and Networks

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List of Illustrations

1 Chapter 1Figure 1.1 The bridges of Königsberg.Figure 1.2 The prism graph.Figure 1.3 An example of a graph, multigraph, digraph, and network.Figure 1.4 Traveling salesman network.Figure 1.5 Strongly connected digraphs.Figure 1.6 Complete graphs.Figure 1.7 Paths, cycles, and wheels.Figure 1.8 Bipartite and tripartite graphs.Figure 1.9 Star graphs.Figure 1.10 Example of trees.Figure 1.11 Subgraphs.Figure 1.12 Two drawings of a planar graph.Figure 1.13 C. elegans connectome.Figure 1.14 C. elegans in‐degree (top) and out‐degree (bottom) distributions...Figure 1.15 Three pairs of isomorphic graphs.Figure 1.16 The non‐isomorphic graphs on

vertices.Figure 1.17 The non‐identical graphs on

vertices.Figure 1.18 Shapes of graphs.Figure 1.19 The Erdős‐1 collaboration graph.Figure 1.20 Two non‐isomorphic graphs and their decks of vertex‐deletions.Figure 1.21 An example of a join.Figure 1.22 Two examples of Cartesian products.Figure 1.23 The four‐dimensional cube.Figure 1.24

and

.Figure 1.25 Examples of complements.Figure 1.26 Examples of a subdivision.Figure 1.27 Line graphs.Figure 1.28 Forbidden induced subgraphs for line graphs.Figure 1.29 Example of edge‐deletions and edge‐contractions.Figure 1.30 Petersen graph.Figure 1.31 Examples of graphs and digraphs.Figure 1.32 Pairs of graphs for isomorphism testing.Figure 1.33 A graph that contains all nine forbidden induced subgraphs for l...

2 Chapter 2Figure 2.1 Non‐isomorphic trees on

vertices.Figure 2.2 Spanning trees.Figure 2.3 An example for Cayley's tree counting theorem.Figure 2.4 A tree with a left and right vertex.Figure 2.5 Eccentricity, diameter, and radius.Figure 2.6 Cut vertices and bridges.Figure 2.7 Cospectral graphs with respect to the adjacency matrix.Figure 2.8 Examples of graphs and digraphs.Figure 2.9 Three pairs of cospectral graphs.

3 Chapter 3Figure 3.1 Customer‐item bipartite graph.Figure 3.2 A graph and a digraph for centrality measures.Figure 3.3 A graph and a digraph.Figure 3.4 Schoch and Brandes graphs.Figure 3.5 A small town map.

4 Chapter 4Figure 4.1

with a standard scale and a log–log scale.Figure 4.2 The in‐degree distribution of the high energy physics citation di...Figure 4.3 Classification of 1958 couples based on race.Figure 4.4 Assortativity function for the Erdős‐1 collaboration graph.Figure 4.5 Regional Schools Network and Organizations Network.

5 Chapter 5Figure 5.1 Step‐by‐step explanation of DFS and BFS.Figure 5.2 Kruskal's and Prim's algorithms.Figure 5.3 A Weighted Digraph.Figure 5.4 Dijkstra's Algorithm.Figure 5.5 Examples of weighted graphs.Figure 5.6 Example of a weighted digraph.

6 Chapter 6Figure 6.1 Hierholzer's algorithm.Figure 6.2 Eulerizing graphs.Figure 6.3 Hamiltonian graphs.Figure 6.4 Kirkman's graph and

.Figure 6.5 Non‐Hamiltonian graphs.Figure 6.6 Closure of a graph.Figure 6.7 Graph coloring.Figure 6.8 Greedy Coloring Algorithm.Figure 6.9 Vertex and edge connectivity.Figure 6.10 Ear decompositions.Figure 6.11 An example for Menger's TheoremFigure 6.12 Deletion and contraction of the edges of

7 Chapter 7Figure 7.1 Stereographic projection.Figure 7.2 Geometric dual.Figure 7.3 Non‐isomorphic graphs with isomorphic geometric duals.Figure 7.4 Schlegel diagram of a cube.Figure 7.5 Graphs that do not correspond to convex polyhedra.Figure 7.6 Platonic solids.Figure 7.7 Tutte's counterexample to Tait's conjecture.Figure 7.8

with 3 edge crossings.Figure 7.9

embedded on the torus.

8 Chapter 8Figure 8.1 Network flows.Figure 8.2 Flow augmenting path.Figure 8.3 Stable sets, matchings, and coverings.Figure 8.4 A system of distinct representatives.Figure 8.5

‐augmenting path.Figure 8.6 Matchings and blossoms.Figure 8.7

‐alternating trees.Figure 8.8 Flower.Figure 8.9 A graph with a matching.Figure 8.10 A graph with a larger matching.

9 4Figure D.1 Example of a stack.Figure D.2 Example of a queue.

Guide

1 Cover Page

2 Table of Contents

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