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| Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians |
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| Ïðåäìåòíûé óêàçàòåëü |
Closed path 442
Closure property 383—384
Code, generation using shift registers 541
Code, Gray 604
Code, Pruefer 495—497
Coefficients in power series 239
Coefficients of generating functions 247—251
Coloring of a graph see "Chromatic numbers"
Combinations see also "Inclusion-exclusion principle of" "Permutations"
Combinations with unlimited repetition 164—169
Combinations, binomial coefficients see "Binomial coefficients"
Combinations, defined 143
Combinations, ordered partitions 177—181 182—184
Combinations, repetition numbers 144 146
Combinations, summary of use 182—184
Combinations, unordered partitions 181—184
Combinations, with constrained repetitions 172—177
Combinations, without repetitions 151—154
Combinatorial circuits see "Switching mechanisms"
Common difference 110
Common ratio 110 249
Commutative binary operation on a set 16
Commutative property of sets 5
Complement of a fuzzy set 705
Complement of a relation 379
Complement of a subgraph 455—456
Complement, absolute, of a set 4
Complete binary tree 509—510
Complete bipartite graph 457 531—532
Complete graph 452—453 531
Complete k-partite graph 467
Complete matching 687 689—691
Complexity of algorithms 407
Components of a graph 472
Composite integer 120
Composition in expert systems 724
Composition of fuzzy relations 713
Composition of relations 382—383
Composition of set relations 14—15
Compound interest as a recurrence relation 274
Computational complexity theory 407
Concentration of a fuzzy set 706
Conclusion 35 47
Conditional proof 62—63 72
Conditional proposition 35
Congruence class of a set 12
Congruence modulo m 354
Congruence modulo n equivalence relation 12
Conjecture 23—24
Conjunction in Boolean algebras 591—592
Conjunction in expert systems 724
Conjunction of propositions 34
Conjunction rule of inference 49
Conjunctive normal form for Boolean expressions 591—592
Connected biparite graph 548
Connected components of a graph 391—392 472
Connected vertices 388 472
Connectives, logical 34—38
Consequent of an implication 35
Consistent postulates 579
Constant term in power series 239
Constructive dilemma 49
Constructive existence proof 87—88
Containment of sets 3—4
Contingency 38
Contracted edge 494
Contradiction 38
Contrapositive, law of 40 41—42
Conventional set, theory 2 see
Conversation equation 638
CONVERSE 37 41—42
Convex combination of fuzzy sets 707—708
Convex fuzzy set 732
Cook, Stephen 406
Correctness of an algorithm 404
Correspondence see "Functions"
Countable sets 367
Counterexample 87
Counting, principles of, applications 134—136
Counting, principles of, disjunctive counting 126—132
Counting, principles of, factorials, defined 136
Counting, principles of, indirect counting 132—133
Counting, principles of, one-to-one correspondence 133—134
Counting, principles of, sequential counting 128—132
Covering of edges 695
Critical planar graph 529
Cross edges 483
Crossing number of a graph 534
Crossover point 701
Crossovers of a graph 523
Cube, edge graph of 458
Cubic graph 439 464—465
Cut edge 472
Cut vertex 472
Cut-set 654—655
Cuts, capacity of 647—648
Cuts, edge cut-set 654—655
Cuts, flow across, net 649
Cuts, minimal 645—652
Cuts, S-D 647—651
Cycle graph 457
Cycles, directed 388
Cycles, Hamiltonian 543—551
Cycles, nondirected 442
Dagger function 593
Data selector see "Multiplexers"
de Bruijn diagrams 540
De Bruijn sequences 539—541
Deficiency of a directed bipartite graph 693
Degree of a vertex 333 439
Degree sequence of a graph 439
DeMorgan's laws 6 40—41 49 50 61 86 584
Denial of a proposition 34
Depth-first search (DFS) 482 485
Derangements 226—228 274
Descendant of a vertex 482
Destructive dilemma 49
Deterministic algorithms 419
Development, stages of 21—22
DFS see "Depth-first search"
Diagonal argument in proofs 377—378
Diagonal edge 548
Diameter of a graph 465
Diaphantus 362
Difference equations see "Recurrence relations"
Difference of relations 379
Digraphs see "Directed graphs"
Dilation of a fuzzy set 706
Dilemma, constructive and destructive 49
Dirac's theorem 551
Dirac, G.A. 561
Direct proof 61 63—64
Direct sum of Boolean algebra 585—586
Directed bipartite graphs, complete matching for 687 689—691
Directed bipartite graphs, deficiency of 693
Directed bipartite graphs, Hall's Marriage Theorem 689—691
Directed bipartite graphs, Koenig's Theorem 695
Directed bipartite graphs, Latin rectangle, square 693
Directed bipartite graphs, matching for 687 688—689
Directed bipartite graphs, maximal matching for 687
Directed forest 500—501
Directed graphs see also "Graphs"
Directed graphs, "degree spectrum" 334
Directed graphs, adjacency matrices 396—402
Directed graphs, antisymmetric 339 340
Directed graphs, asymmetric 339 340
Directed graphs, Boolean matrices 396—402
Directed graphs, capacity function 633
Directed graphs, circuit 388
Directed graphs, connected component 391—392
| Directed graphs, cut-set 654—655
Directed graphs, cycle 388
Directed graphs, defined 332 437
Directed graphs, directed path 388
Directed graphs, disconnecting set 654
Directed graphs, edges see "Edges of graphs"
Directed graphs, endpoints 388
Directed graphs, invariant 334
Directed graphs, irreflexive 339 340
Directed graphs, isomorphic 334—335
Directed graphs, labeling 632—633 636
Directed graphs, loop-free 333
Directed graphs, Menger's Theorem 695
Directed graphs, networks see "Networks"
Directed graphs, nontrivial path 388—389
Directed graphs, paths see "Paths in graphs"
Directed graphs, reflexive 339 340
Directed graphs, simple 333
Directed graphs, simple path 388
Directed graphs, strongly connected vertices 391—392
Directed graphs, symmetric 339 340 438
Directed graphs, transitive 339—340
Directed graphs, transport networks see "Networks"
Directed graphs, unilaterally connected vertices 391—392
Directed graphs, vertices see "Vertices of graphs"
Directed graphs, viewed as nondirected graphs 438—439
Directed graphs, weakly connected vertices 391—392
Directed multigraph 333
Directed path 388
Directed spanning tree 480
Directed trees 468—470 498—504
Directed trees, full 506
Directed trees, ordered 517
Directed trees, regular 505
Directed trees, thin 506
Disconnecting set of edges 654
Discovery, aspects of 21—22
Disjoint sets 5 211
Disjunction in Boolean algebras 591—592
Disjunction in expert systems 724
Disjunction of propositions 34
Disjunctive counting 126—132
Disjunctive normal form for Boolean expressions 591—592
Disjunctive syllogism 49
Disposition 722
Distinct representatives, system of 657 686
Distinctive-shape logic symbols 601—602
Distribution, possibility 715—720
Distributive laws for sets 5
Divide-and-conquer relations 285 321—322
Divisibility tests 359—360
Division of formal power series 247—251
Dodecahedron, edge graph of 458
Dodecahedron, Hamilton's game 543
Domain in the FRKB 725
Domain of relation on a set 10—11
Double negation, law of 40
Dual graph of a plane graph 526—527
Dual graph, vertices of 569
Dual of a poset 370
Economy tree 486
Edge cut-set 654—655
Edge labeling of a graph 444
Edge-disjoint paths 442
Edges of graphs, adjacent to 333
Edges of graphs, backward 666
Edges of graphs, between vertices 437
Edges of graphs, bridge 472 541
Edges of graphs, capacity constraint 638
Edges of graphs, capacity of 633—634 647—648
Edges of graphs, circuit 388
Edges of graphs, complete matching 687 689—691
Edges of graphs, contracted 494
Edges of graphs, conversation equation 638
Edges of graphs, cross 483
Edges of graphs, crossovers 523
Edges of graphs, cube 458
Edges of graphs, cut edge 472
Edges of graphs, cut-set 654—655
Edges of graphs, cycle 388
Edges of graphs, defined 332
Edges of graphs, diagonal 548
Edges of graphs, disconnecting set 654
Edges of graphs, dodecahedron 458
Edges of graphs, edge cut-set 654—655
Edges of graphs, endpoints 388
Edges of graphs, flow across see "Flows in Net-works"
Edges of graphs, forward 666
Edges of graphs, hyperedges 728—731
Edges of graphs, icosahedron 458
Edges of graphs, incident from, on, to 333 439
Edges of graphs, joining vertices 437
Edges of graphs, labeling 632—633 636
Edges of graphs, left, in binary tree 507
Edges of graphs, loop 333 437
Edges of graphs, matching 687 688—689
Edges of graphs, maximal matching 687
Edges of graphs, minimal cut 645—652
Edges of graphs, multiple 333
Edges of graphs, multiplicities 535—536
Edges of graphs, nondirected path 388
Edges of graphs, octahedron 458
Edges of graphs, platonic solids 458
Edges of graphs, reverse 666
Edges of graphs, right, in binary tree 507
Edges of graphs, S-D cut 647—651
Edges of graphs, saturated 639
Edges of graphs, self-loop 437
Edges of graphs, simple path 388
Edges of graphs, slack of 639
Edges of graphs, tetrahedron 458
Edges of graphs, tree 483
Edges of graphs, unsaturated 639
Edges of graphs, vertex covering of 695
Edison, Thomas A. 18
Edmonds 671
Education stage of development 21
Efficiency of algorithms 404—407
Egervary 689
EKB see "Explanatory knowledge base"
Elements (Euclid's) 20
Elements of a set 1
Elements of an argument 19—20
Empty set 4
Endpoints of a path 388
Enumeration of sets 367—368
Enumeration, ordering of strings 375
Enumeration, topological 428—432
Equality of generating functions 240
Equality of sets 4
Equivalence class 350—351
Equivalence class for integers 354—358
Equivalence class, canonical representative 356
Equivalence relations 340
Equivalence relations on integers 354—358
Equivalence relations on sets 11
Equivalence relations, defined 350
Equivalence relations, equivalence class 350—351
Equivalences of expressions 85—86
Equivalent propositional functions 38
Equivalent switching mechanisms 596
Equivocation, fallacy of 28
Eratosthenes (Sieve of) 224—225
ES see "Expert systems"
Euclid 20
Euclid's Elements 20
Euclid's lemma 360
Euclidean algorithm 78 117
Euclidean plane 15
Euclidean prime 118
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