Discrete Mathematics: Elementary and Beyond

288 Index

transitivity, 106
conjecture, 68
convex polygon, 179, 191
countries of a map, 189
cryptography, 110, 122, 242
cryptosystem, 242
cube, 194
Cube space, 215, 221, 224, 236
cut-edge, 142
cycle, 131, 141
Hamiltonian, 139, 161
length, 131
odd, 201

decrypt, 242
definition by induction, 66
degree of a node, 143, 150, 155,
195
difference of sets, 6
Digital Encryption Standard, 250
disjoint, 6
divisor, 87
dodecahedron, 194
graph, 139
double star, 155

edge, 126
parallel, 126
element of a set, 4
encoding, 11
encrypt, 242
Erd ̋os, P ́al, 184
Euclid’s Fifth Postulate, 213
Euclidean Algorithm, 99–104, 112,
123, 249
Euler’s Formula, 189–191, 194–
196, 208
Euler, L., 135
event, 77
exclusive, 78
experiment, 77

face of a map, 194
factorization, 90, 99, 122
Fano, G., 217

father code, 149

Fermat test, 117

general, 120

Fermat’s “Little” Theorem, 97–

99, 117, 121, 248

Fermat, Pierre de, 97

Fibonacci numbers, 65–75, 83,

102, 123

Fibonacci, Leonardo, 65

Fisher’s Inequality, 223

Five Color Theorem, 207

floor, 15

Four Color Theorem, 206

Frobenius, G., 169

Fundamental Theorem of Arith-

metic, 90

Gauss curve, 57

Gauss, C.F., 105

general position, 182

Goldbach’s conjecture, 96

golden ratio, 74

graph, 126, 189

k-colorable, 202

2-colorable, 200

bipartite, 165, 195, 200, 223

complement, 130

complete, 130, 192

connected, 131, 142

connected component, 133

dual, 206

edgeless, 130

planar, 192, 206–208

simple, 126

greatest common divisor, 99

Guthrie, F., 206

Hall, P., 169

Happy End Problem, 184

https, 250

icosahedron, 194

Inclusion–Exclusion Formula, 34,

114

independent events, 79