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| Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction |
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| Предметный указатель |
Graph theory infinite region 564
Graph theory Instant Insanity 541—544
Graph theory isolated vertex 363 374 530
Graph theory k(G), the number of components of G 534
Graph theory k-regular graph 551
Graph theory Konigsberg 396 551—553 598
Graph theory Kuratowski’s Theorem 563 599
Graph theory L(G) 605
Graph theory tree 598
Graph theory trivial walk 531
Graph theory vertices 363 530
Graph theory walk 531 532
Graph theory,  554
Graph theory, 2-isomorphic graphs 576
Graph theory, digraph 363 530
Graph theory, disconnected graph 366 533
Graph theory, induced subgraph 539
Graph theory, intersection of graphs 594
Graph theory, isomorphic graphs 544
Graph theory, labeled multigraph 542
Graph theory, ladder graph 604 654
Graph theory, length of a cycle 365
Graph theory, length of a path 365
Graph theory, length of a walk 531
Graph theory, line graph 605
Graph theory, loop 363 365 367 368 373 530 543 550 569 571
Graph theory, loop-free graph 365 530
Graph theory, maximal independent set 587 655
Graph theory, minimal covering of a graph 603
Graph theory, minimal dominating set 603 757
Graph theory, multigraph 363 534 542
Graph theory, multiplicity (of an edge) 534
Graph theory, n-cube 602
Graph theory, n-graph 534
Graph theory, nodes 363 530
Graph theory, nonplanar graph 560—563
Graph theory, null graph 541
Graph theory, one-factor 692
Graph theory, one-terminal-pair-graph 572
Graph theory, open walk 531
Graph theory, origin (of an edge) 363 530
Graph theory, out degree (of a vertex) 554
Graph theory, outgoing degree (of a vertex) 554
Graph theory, path 365 532 533
Graph theory, pendant vertex 550 569
Graph theory, perfect matching 692
Graph theory, Petersen graph 563 590 600
Graph theory, planar graph 560 645
Graph theory, planar-one-terminal-pair-graph 572
Graph theory, planarity of graphs 366
Graph theory, Platonic solids 567 568
Graph theory, Polya’s theory of enumeration 600
Graph theory, precedence graph 364
Graph theory, proper coloring of a graph 588
Graph theory, regions (in a planar graph) 563
Graph theory, regular graph 550
Graph theory, rooted binary tree 499 500
Graph theory, rooted ordered binary tree 500 505—507
Graph theory, round-robin tournament 582
Graph theory, self-complementary graph 549
Graph theory, Seven Bridges of Konigsberg 396 551—553 598
Graph theory, source (of an edge) 363 530
Graph theory, spanning subgraph 538
Graph theory, spokes 537
Graph theory, square of a graph 653
Graph theory, strongly connected graph 365 558
Graph theory, subgraph 538
Graph theory, terminals 572
Graph theory, terminating vertex 363 530
Graph theory, terminus (of an edge) 363 530
Graph theory, tournament 581
Graph theory, trail 532 533
Graph theory, Traveling Salesman Problem 585 600
Graph theory, undirected edge 363
Graph theory, undirected graph 364 530
Graph theory, union of graphs 594
Graph theory, utility graph 561
Graph theory, vertex 363
Graph theory, vertex degree 550
Graph theory, weight of an edge 657
Graph theory, weighted graph 657
Graph theory, wheel graph 537
Gray code 587
Greatest common divisor for integers 225—228 231 238
Greatest common divisor for polynomials 844 845
Greatest element (in a poset) 377
Greatest integer function ([x]) 252 253 406 629
Greatest lower bound (gib) 378
Greedy algorithm 658 665 667 669 694
Gregory, Duncan 176
Griess, Robert, Jr. 831
Group 777
Group acting on a set 816
Group code 806 (see also “Algebraic coding theory”)
Group homomorphism 785
Group isomorphism 785
Group of permutations 783 815 872
Group of rigid motions of a cube 826 827
Group of rigid motions of a regular hexagon 822 823
Group of rigid motions of a regular tetrahedron 827 828
Group of rigid motions of a square 814
Group of rigid motions of an equilateral triangle 781—783
Group of transformations 829 831
Group of units 779
Group theory 777—834
Group theory  783
Group theory, abelian group 777
Group theory, algebraic coding theory 806—810
Group theory, center 784
Group theory, commutative group 777
Group theory, coset 791 830
Group theory, cyclic group 787 789
Group theory, decomposition of a permutation 815
Group theory, definition of a group 777
Group theory, direct product of groups 783
Group theory, Euler’s Theorem on Congruence 792
Group theory, Fermat’s Theorem on Congruence 792
Group theory, fixed (invariant) 817
Group theory, generator of a (sub)group 787
Group theory, group acting on a set 816
Group theory, group of permutations 783 815 872
Group theory, group of transformations 829 831
Group theory, group of units 779
Group theory, homomorphism 785
Group theory, invariant element under a permutation 815 817
Group theory, isomorphism 785
Group theory, kernel of a homomorphism 833
Group theory, Klein Four group 789
Group theory, Lagrange’s Theorem 792
Group theory, left coset 791
Group theory, length of a cycle 815
Group theory, multiples of group elements 780
Group theory, nontrivial subgroup 780
Group theory, normal subgroup 831 872
Group theory, order of a group 778
Group theory, order of a group element 787 788
Group theory, Polya’s method of enumeration 812—828
Group theory, powers of group elements 780
Group theory, product of disjoint cycles 814
Group theory, proper subgroup 780
Group theory, right coset 791
Group theory, rigid motions of a cube 826 827
Group theory, rigid motions of a regular hexagon 822 823
Group theory, rigid motions of a regular tetrahedron 827 828
Group theory, rigid motions of a square 814
Group theory, rigid motions of an equilateral triangle 781—783
Group theory, simple group 831
Group theory, solvable group 872
Group theory, stabilizer 820
Group theory, subgroup 780 781
| Group theory, symmetric group 783
Group theory, trivial subgroup 780
Grundlagen der Mathematik 139
Gruppentheoretischen Studien II 830
Guthrie, Francis 589 599
Guthrie, Frederick 589
Guy, Richard K. 522 524
Haken, Wolfgang 589 599—601
half-adder 746 747
Half-open interval 153
Hall, Marshall, Jr. 429 873
Hall, Philip 684 687 695
Hall’s Marriage Condition 689
Halmos, Paul R. 179 A-37
Hamilton cycle 578—585 599 600
Hamilton path 578—585 599
Hamilton, Sir William Rowan 176 578 589 599
Hamming bound 806 (see also “Algebraic coding theory”)
Hamming code 811 (see also “Algebraic coding theory”)
Hamming matrix 811 (see also “Algebraic coding theory”)
Hamming metric 799 (see also “Algebraic coding theory”)
Hamming, Richard Wesley 793 794 798 831 832
Hanson, Dems 429
Harary, Frank 599—602 651 652
Hardy, Godfrey Harold 241 429
Harmonic numbers 183 192 193 200 206 207
Hartsfield, Nora 599 602
Harvard University Computation Laboratory 772 773
Hashing function 701 720 721 732
Hasse diagram 373—376 394 765—768
Hasse, Helmut 394
Hdhere Algebra 394
Heath, Thomas Little 44 46
Heawood, Percy John 589
Height of a rooted tree 629
Hell, Pavol 670 694 696
Henle, James M. 179 A-37
Herschel graph 587 590
Herstein, Israel Nathan 831 832 872 873
Hexadecimal notation 219 220
Hilbert, David 139 178 260 343 731
Hill, Frederick J. 773
History of enumeration 44
Hodges, Andrew 344
Hoggatt, Verner E., Jr. 522 524
Hohn, Franz E. 343 344 811 831 832
Homeomorphic graphs 562
Homer’s method 308
Homogeneous recurrence relations 463 471 483
Homomorphism of groups 785
Homomorphism of rings 723
Honsberger, Ross 522—524
Hopcroft, John E. 343 344 395 396 523 600 601 651 652 670 694 695 732
Hopper, Grace 651
Horowitz, Ellis 668 670 694 696
Hubert decision problem 344
Huffman tree 642 643
Huffman, David Albert 343 345 396 641 651 652
Huffman’s construction for optimal tree 641—643
Hungarian method 695
Huygens, Christiaan 45
Hypothesis 52
I Principii di Geometrica 395
I-node 17
IBM PORT 5
icosahedron 568
Ideal 714 725 731
Idempotent Law of Addition 750 752 760
Idempotent Laws for a Boolean algebra 763
Idempotent Laws for Boolean functions 737
Idempotent Laws for Boolean variables 737
Idempotent Laws for logic 65
Idempotent Laws for set theory 160
Identity element for + in a ring 702
Identity element for a binary operation 269 270
Identity element for concatenation 318
Identity element of a group 777
Identity for the addition of real numbers 119 120
Identity for the multiplication of real numbers 120
Identity function 280
Identity laws for a Boolean algebra 762
Identity laws for Boolean functions 737
Identity laws for Boolean variables 737
Identity laws for logic 65
Identity laws for set theory 160
If and only if 53
If p, then q 52
If-then decision structure 55
If-then-else decision structure 55
IFF 53
Image of a set 256
Image of an element 251
Implication 52 56 58 121—123
Implicit quantification 112
Implicit quantifiers 102 103
Implies 52
In degree of a vertex 554
Incidence matrix for a design 874
Incidence matrix for a graph 559
incident 530
Inclusive or 52
Incoming degree of a vertex 554
Incompletely specified Boolean function 758
Increasing function 313
Independence (and Boolean variables) 744
Independence number of a graph 587
Independent 820
Independent events 794
Independent outcome 173
Independent set of vertices 587 655
Independent solutions see “Linearly independent solutions”
Independent switches 72 73
Indeterminate 835
Indeterminate form A-2
INDEX 166
Index list 397
Index of a product 235
Index of a summation 22
Index set 166
Indirect block 17
Indirect method of proof 93
Indirect proof 134
Induced subgraph 539
Induction hypothesis 186 197
Inductive step 185 186 196
Infeld, Leopold 872 873
Infinite cardinal numbers A-35 A-36
Infinite region 564
Infinite sequence A-30
Infinite set 144 309 311 A-28
Infix notation 249 619
Information retrieval 720
Initial condition(s) 462
Injective function 255
Inorder traversal 622
Input (for a finite state machine) 328
Input (for a gate) 745 746
Input (for an algorithm) 227 293
Input (function) 252
Input alphabet 328
Instant Insanity 541—544
INT (greatest integer function) 253
Integers modulo n 717—721
Integral domain 706 711 837—839 850
Internal states 315 328 349 388
Internal vertices 614
International Business Machines Corporation 5
Intersection of graphs 594
Intersection of sets 157 159
Introductio in Analysin Infinitorum 456
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