Index Index
\((n,k)\) code, Notation
\(k\)-colourable, Definition
\(k\)-critical, Definition
\(k\)-edge-colourable, Definition
\(k\)-planar, Paragraph
\(n\) choose \(r\), Definition
\(n\) factorial, Definition
\(r\)-combination, Definition
\(r\)-permutation, Definition
\(t\)-\((v,k,\lambda)\) design, Definition
\(u-v\) walk, Definition
balanced, Definition
balanced incomplete block design (BIBD), Definition
base case, Definition
Bell number, Definition
binary linear code, Definition
binomial coefficients, Definition
generalised, Definition
Binomial Theorem, Theorem
Generalised, Theorem
bipartite, Definition
complete bipartite graph, Definition
bipartition, Definition
bits, Assumption
block-intersection graph, Paragraph
blocks, Definition
bridge, Definition
Brooks' Theorem, Theorem
Catalan number, Definition
choose
\(n\) choose \(r\), Definition
chromatic index, Definition
chromatic number, Definition
class-one graph, Definition
class-two graph, Definition
closed, Definition
closure, Definition
code, Paragraph
codewords, Paragraph
colourable
\(k\)-colourable, Definition
colouring
proper \(k\)-colouring, Definition
column vector, Notation
combination
\(r\)-combination, Definition
combinatorial identity, Definition
combinatorial proof, Definition
Combinatorial Proofs, Theorem
complement, Definition Definition
complementary design, Definition
complete bipartite graph, Definition
complete graph, Definition
complex conjugate, Paragraph
connected, Definition
connected component, Definition
contracting the edge \(uv\), Definition
critical
\(k\)-critical, Definition
cubic graph, Definition
cycle, Definition
degree, Definition
degree sequence, Item
delete the edge \(e\), Definition
delete the vertex \(v\), Definition
derangement, Definition
design, Definition
\(t\)-\((v,k,\lambda)\) design, Definition
resolvable, Definition
difference collection, Definition
difference set, Definition
digraph, Definition
directed graph, Definition
distinguishing cost, Definition
distinguishing number, Definition
dual graph, Definition
edge
subdivided, Definition
edge chromatic number, Definition
edge-colourable
\(k\)-edge-colourable, Definition
edge-colouring
proper \(k\)-edge-colouring, Definition
edges, Definition
multiple edge, multiedge, Definition
endvertices, Definition
equivalence relation, Paragraph
Erdős-Rényi random graph model, Definition
Erdős-Szekeres Theorem, Theorem
Euler tour, Definition
Euler trail, Definition
Euler's Formula, Theorem
Euler's handshaking lemma, Lemma
for digraphs, Lemma
Euler's handshaking lemma for digraphs, Lemma
Even more generalised pigeonhole principle, Proposition
exponential generating function, Definition
faces, Definition
factorial
\(n\) factorial, Definition
Fibonacci sequence, Definition
Fisher's Inequality, Theorem
Five-Colour Theorem, Theorem
forest, Definition
Four-Colour Theorem, Theorem
generalised binomial coefficient, Definition
Generalised Binomial Theorem, Theorem
Generalised Pigeonhole Principle, Proposition
generating function, Definition
exponential, Definition
generator matrix, Example Paragraphs
Gilbert random graph model, Definition
graph, Definition
directed graph, digraph, Definition
simple, Definition
Hall's Theorem, Theorem
Hamilton cycle, Definition
Hamilton path, Definition
Hamilton-connected, Item
Hamming code, Remark
Hamming distance, Definition
hypercube, Definition
improvement, Definition
incident with, Definition
incident with a face, Definition
Inclusion-Exclusion, Theorem
indegree, Definition
induced subgraph, Definition
induction
base case, Definition
inductive hypothesis, Definition
inductive step, Definition
inductive hypothesis, Definition
inductive step, Definition
initial conditions, Definition
invalency, Definition
isolated vertex, Definition
isomorphic, Definition
isomorphism, Definition
maximum valency, Definition
minimum distance, Definition
minimum valency, Definition
minor, Definition
modulo \(n\), Definition
multiedge, Definition
multigraph, Definition
multiple edge, Definition
mutually orthogonal, Definition
neighbour, Definition
parallel, Definition
parity-check matrix, Definition
partial fractions, Example
partition, Paragraph
path, Definition
perfect graph, Definition
permutation, Definition
\(r\)-permutation, Definition
Petersen graph, Example
Pigeonhole Principle, Proposition
even more generalised, Proposition
Generalised, Proposition
planar, Definition
planar dual, Definition
planar embedding, Definition
Praeger-Xu graph, Definition
preserve the colouring, Definition
Principle of Mathematical Induction, Theorem
Product Rule, Theorem
for many aspects, Theorem
Product Rule for many aspects, Theorem
projective plane, Definition
proper, Definition
proper \(k\)-edge-colouring, Definition
proper \(k\)-vertex-colouring, Definition
Ramsey number, Item
Ramsey's Theorem, Theorem
recursion
initial conditions, Definition
recursive relation, Definition
recursive relation, Definition
recursively defined, Definition
reflexive, Item
regular, Definition
resolvable design, Definition
self-dual, Item
sequence
recursively defined, Definition
simple graph, Definition
snark, Definition
Steiner system, Definition
Steiner triple system, Definition
Strong Induction, Theorem
Strong Perfect Graph Theorem, Theorem
subdivided, Definition
subdivision, Definition
subgraph, Definition
proper, Definition
Sum Rule, Theorem
for many cases, Theorem
Sum Rule for many cases, Theorem
symmetric, Item
system of distinct representatives (SDR), Definition
there is a blue copy of \(K_\ell\), Item
there is a red copy of \(K_k\), Item
tour, Definition
trail, Definition
transitive, Item
tree, Definition
triangle inequality, Remark
triple system, Definition
Kirkman, Definition
Steiner, Definition
type \((n,k)\), Notation
uniform, Definition
Wagner's Theorem, Theorem
walk, Definition
\(u-v\) walk, Definition
closed, Definition
Wilson's Theorem, Theorem