| Preface to the first edition | p. xi |
| Preface to the second edition | p. xiii |
| Graphs | p. 1 |
| Terminology of graphs and digraphs | |
| Eulerian circuits | |
| Hamiltonian circuits | |
| Trees | p. 12 |
| Cayley's theorem | |
| Spanning trees and the greedy algorithm | |
| Search trees | |
| Strong connectivity | |
| Colorings of graphs and Ramsey's theorem | p. 24 |
| Brooks' theorem | |
| Ramsey's theorem and Ramsey numbers | |
| The Lovasz sieve | |
| The Erdos-Szekeres theorem | |
| Turan's theorem and extremal graphs | p. 37 |
| Turan's theorem and extremal graph theory | |
| Systems of distinct representatives | p. 43 |
| Bipartite graphs | |
| P. Hall's condition | |
| SDRs | |
| Konig's theorem | |
| Birkhoff's theorem | |
| Dilworth's theorem and extremal set theory | p. 53 |
| Partially ordered sets | |
| Dilworth's theorem | |
| Sperner's theorem | |
| Symmetric chains | |
| The Erdos-Ko-Rado theorem | |
| Flows in networks | p. 61 |
| The Ford-Fulkerson theorem | |
| The integrality theorem | |
| A generalization of Birkhoff's theorem | |
| Circulations | |
| De Bruijn sequences | p. 71 |
| The number of De Bruijn sequences | |
| Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme | p. 77 |
| Quadratic forms | |
| Winkler's theorem | |
| Associative block designs | |
| The principle of inclusion and exclusion; inversion formulae | p. 89 |
| Inclusion-exclusion | |
| Derangements | |
| Euler indicator | |
| Mobius function | |
| Mobius inversion | |
| Burnside's lemma | |
| Probleme des menages | |
| Permanents | p. 98 |
| Bounds on permanents | |
| Schrijver's proof of the Minc conjecture | |
| Fekete's lemma | |
| Permanents of doubly stochastic matrices | |
| The Van der Waerden conjecture | p. 110 |
| The early results of Marcus and Newman | |
| London's theorem | |
| Egoritsjev's proof | |
| Elementary counting; Stirling numbers | p. 119 |
| Stirling numbers of the first and second kind | |
| Bell numbers | |
| Generating functions | |
| Recursions and generating functions | p. 129 |
| Elementary recurrences | |
| Catalan numbers | |
| Counting of trees | |
| Joyal theory | |
| Lagrange inversion | |
| Partitions | p. 152 |
| The function P[subscript k] (n) | |
| The partition function | |
| Ferrers diagrams | |
| Euler's identity | |
| Asymptotics | |
| The Jacobi triple product identity | |
| Young tableaux and the hook formula | |
| (0, 1)-Matrices | p. 169 |
| Matrices with given line sums | |
| Counting (0, 1)-matrices | |
| Latin squares | p. 182 |
| Orthogonal arrays | |
| Conjugates and isomorphism | |
| Partial and incomplete Latin squares | |
| Counting Latin squares | |
| The Evans conjecture | |
| The Dinitz conjecture | |
| Hadamard matrices, Reed--Muller codes | p. 199 |
| Hadamard matrices and conference matrices | |
| Recursive constructions | |
| Paley matrices | |
| Williamson's method | |
| Excess of a Hadamard matrix | |
| First order Reed-Muller codes | |
| Designs | p. 215 |
| The Erdos-De Bruijn theorem | |
| Steiner systems | |
| Balanced incomplete block designs | |
| Hadamard designs | |
| Counting | |
| (higher) incidence matrices | |
| The Wilson--Petrenjuk theorem | |
| Symmetric designs | |
| Projective planes | |
| Derived and residual designs | |
| The Bruck--Ryser--Chowla theorem | |
| Constructions of Steiner triple systems | |
| Write-once memories | |
| Codes and designs | p. 244 |
| Terminology of coding theory | |
| The Hamming bound | |
| The Singleton bound | |
| Weight enumerators and MacWilliams' theorem | |
| The Assmus--Mattson theorem | |
| Symmetry codes | |
| The Golay codes | |
| Codes from projective planes | |
| Strongly regular graphs and partial geometries | p. 261 |
| The Bose--Mesner algebra | |
| Eigenvalues | |
| The integrality condition | |
| Quasisymmetric designs | |
| The Krein condition | |
| The absolute bound | |
| Uniqueness theorems | |
| Partial geometries | |
| Examples | |
| Directed strongly regular graphs | |
| Neighborhood regular graphs | |
| Orthogonal Latin squares | p. 283 |
| Pairwise orthogonal Latin squares and nets | |
| Euler's conjecture | |
| The Bose--Parker--Shrikhande theorem | |
| Asymptotic existence | |
| Orthogonal arrays and transversal designs | |
| Difference methods | |
| Orthogonal subsquares | |
| Projective and combinatorial geometries | p. 303 |
| Projective and affine geometries | |
| Duality | |
| Pasch's axiom | |
| Desargues' theorem | |
| Combinatorial geometries | |
| Geometric lattices | |
| Greene's theorem | |
| Gaussian numbers and q-analogues | p. 325 |
| Chains in the lattice of subspaces | |
| q-analogue of Sperner's theorem | |
| Interpretation of the coefficients of the Gaussian polynomials | |
| Spreads | |
| Lattices and Mobius inversion | p. 333 |
| The incidence algebra of a poset | |
| The Mobius function | |
| Chromatic polynomial of a graph | |
| Weisner's theorem | |
| Complementing permutations of geometric lattices | |
| Connected labeled graphs | |
| MDS codes | |
| Combinatorial designs and projective geometries | p. 351 |
| Arcs and subplanes in projective planes | |
| Blocking sets | |
| Quadratic and Hermitian forms | |
| Unitals | |
| Generalized quadrangles | |
| Mobius planes | |
| Difference sets and automorphisms | p. 369 |
| Block's lemma | |
| Automorphisms of symmetric designs | |
| Paley--Todd and Stanton--Sprott difference sets | |
| Singer's theorem | |
| Difference sets and the group ring | p. 383 |
| The Multiplier Theorem and extensions | |
| Homomorphisms and further necessary conditions | |
| Codes and symmetric designs | p. 396 |
| The sequence of codes of a symmetric design | |
| Wilbrink's theorem | |
| Association schemes | p. 405 |
| Examples | |
| The eigenmatrices and orthogonality relations | |
| Formal duality | |
| The distribution vector of a subset | |
| Delsarte's inequalities | |
| Polynomial schemes | |
| Perfect codes and tight designs | |
| (More) algebraic techniques in graph theory | p. 432 |
| Tournaments and the Graham--Pollak theorem | |
| The spectrum of a graph | |
| Hoffman's theorem | |
| Shannon capacity | |
| Applications of interlacing and Perron--Frobenius | |
| Graph connectivity | p. 451 |
| Vertex connectivity | |
| Menger's theorem | |
| Tutte connectivity | |
| Planarity and coloring | p. 459 |
| The chromatic polynomial | |
| Kuratowski's theorem | |
| Euler's formula | |
| The Five Color Theorem | |
| List-colorings | |
| Whitney Duality | p. 472 |
| Whitney duality | |
| Circuits and cutsets | |
| MacLane's theorem | |
| Embeddings of graphs on surfaces | p. 491 |
| Embeddings on arbitrary surfaces | |
| The Ringel--Youngs theorem | |
| The Heawood conjecture | |
| The Edmonds embedding technique | |
| Electrical networks and squared squares | p. 507 |
| The matrix-tree theorem | |
| De Bruijn sequences | |
| The network of a squared rectangle | |
| Kirchhoff's theorem | |
| Polya theory of counting | p. 522 |
| The cycle index of a permutation group | |
| Counting orbits | |
| Weights | |
| Necklaces | |
| The symmetric group | |
| Stirling numbers | |
| Baranyai's theorem | p. 536 |
| One-factorizations of complete graphs and complete designs | |
| Hints and comments on problems | p. 542 |
| Hints | |
| Suggestions | |
| Comments on the problems in each chapter | |
| Formal power series | p. 578 |
| Formal power series ring | |
| Formal derivatives | |
| Inverse functions | |
| Residues | |
| The Lagrange--Burmann formula | |
| Name Index | p. 584 |
| Subject Index | p. 590 |
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