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Solutions to A First Course in Graph Theory using

Mathematica

Colophon

Benefits of using Mathematica: typesetting, helping with mechanics of solution, empirical testing of hypothetical solutions.

Visualization and interaction help in understanding.

Taxonomy

Graph "Walk", "Trail", "Circuit", "Path", "Cycle", "Eulerian trail", "Eulerian circuit", "Hamiltonian path", "Hamiltonian cycle" "Trail" "Walk", "Circuit" "Trail", "Path" "Walk", "Cycle" "Circuit", "Cycle" "Path", "Eulerian trail" "Trail", "Eulerian circuit" "Circuit", "Eulerian circuit" "Eulerian trail", "Hamiltonian path" "Path", "Hamiltonian cycle" "Cycle", "Hamiltonian cycle" "Hamiltonian path"

VertexLabels

"Name",

VertexCoordinates

0, 0 1, 1 1, 2 1, 1 0, 3 2, 2 2, 3 2, 2 2, 4 Walk Trail

Circuit

Path Cycle

Eulerian trail

Eulerian circuit

Hamiltonian path

Hamiltonian cycle

2 Graph Theory.nb

1 Introduction

1.1 Graphs and Graph Models

1.3 f S _]

UndirectedEdge

DeleteDuplicates

deleting pairs of the same elements Sort

Select

Select

list of pairs of elements from S whose elements are not the same

Flatten

Table i, j i, S j, S 1 Apply

Unequal

those whose sum is in S or absolute difference is in S

MemberQ

S, Total

MemberQ

S, Abs

1 2 Graph f

2, 3, 4, 7, 11, 13

, VertexLabels "Name" 2 4 11 13 3 7 1.4 Graph f 6,

3, 0, 3, 6

, VertexLabels "Name", ImageSize Small 6 30
3 6

Graph Theory.nb 3

1.5 Graph f Table i i, i, 50 , VertexLabels "Name" 9 16 25
144
169
36
64
100
49
576
625
225
289
81
1600
1681
676
256
400
1225
1369
196
2304
2500
1296
1521
900
1156
324
441
841
784
1024
729
2025
1.7a shift : horizontal moves of black coin

AdjacencyMatrix

Graph Range 12 1 3, 2 4, 7 8, 9 10 horizontal moves of white coin

AdjacencyMatrix

Graph Range 12 1 2, 3 4, 7 9, 8 10 vertical moves of black coin

AdjacencyMatrix

Graph Range 12 1 12, 4 6, 5 7, 10 11 vertical moves of white coin

AdjacencyMatrix

Graph Range 12 1 11, 4 5, 6 7, 10 12 swap : swap of coins

AdjacencyMatrix

Graph Range 12 1 7, 2 8, 3 9, 4 10, 5 11, 6 12

AdjacencyGraph

shift.swap, VertexLabels Table i c i i, 12 , ImageSize Small c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10 c 11 c 12

4 Graph Theory.nb

Graph

Catenate

first moves in orange edges

Property

, EdgeStyle

Orange

EdgeList

AdjacencyGraph

shift second moves in green edges

Property

, EdgeStyle Green

EdgeList

AdjacencyGraph

swap compoound move with thick edges

Property

, EdgeStyle Thick

EdgeList

AdjacencyGraph

shift.swap

VertexLabels

Table i c i i, 12 , GraphLayout "CircularEmbedding" c 1 c 2 c 3 c 11 c 12 c 4 c 5 c 6 c 7 c 8 c 9 c 10 1.7a obtain the text of "As You Like It" text

URLFetch

"http: www.gutenberg.org cache epub 1121
pg1121.txt" tokenize to a list of words stream

StringToStream

text words

ReadList

stream, Word,

WordSeparators

FromCharacterCode

List Join non alphabetic ASCII characters Range

32, 64

, Range

91, 96

Graph Theory.nb 5

Close[stream];

extract three letter words, convert to upper case, and remove duplicates words3

DeleteDuplicates

ToUpperCase

Select

words, StringLength 3 & Graph words3,

Flatten

remove nesting introduced by Table Join join character substitution relations with permutation relations Table substitutions over each of the characters in a word

Property

quotesdbs_dbs17.pdfusesText_23