| Symbol |
Description |
Location |
| \(n!\) |
\(n\) factorial |
Notation 3.1.4 |
| \(\binom{n}{r}\) |
\(n\) choose \(r\) |
Notation 3.2.4 |
| \(\multiset{n}{r}\) |
\(n\) multichoose \(r\) |
Notation 5.1.4 |
| \(\binom{n}{r_1,\ldots,r_m}\) |
\(n\) choose \(r_1\) and \(\ldots\) and \(r_m\) |
Notation 5.2.3 |
| \(\hbox{(IH)}\) |
Inductive Hypothesis |
Definition 6.2.2 |
| \(V\) |
set of vertices of a graph |
Definition |
| \(E\) |
set of edges of a graph |
Definition |
| \(E(G)\) |
edge set of the graph \(G\) |
Definition 11.2.1 |
| \(V(G)\) |
vertex set of the graph \(G\) |
Definition 11.2.1 |
| \(u \sim v\) |
\(u\) is adjacent to \(v\) |
Notation 11.2.5 |
| \(uv\) |
the edge between vertices \(u\) and \(v\) |
Notation 11.2.5 |
| \(\hbox{val}(v)\) |
valency of \(v\) |
Notation 11.2.8 |
| \(\hbox{deg}(v)\) |
valency (degree) of \(v\) |
Notation 11.2.8 |
| \(d(v)\) |
valency (degree) of \(v\) |
Notation 11.2.8 |
| \(d_G(v)\) |
valency (degree) of \(v\) in \(G\) |
Notation 11.2.8 |
| \(G\setminus\{v\}\) |
\(G\) with vertex \(v\) deleted |
Notation 11.3.2 |
| \(G\setminus S\) |
\(G\) with the set \(S\) of vertices deleted |
Notation 11.3.2 |
| \(G\setminus\{e\}\) |
\(G\) with edge \(e\) deleted |
Notation 11.3.4 |
| \(K_n\) |
complete graph on \(n\) vertices |
Definition 11.3.8 |
| \(G^c\) |
complement of \(G\) |
Definition 11.3.10 |
| \(\varphi\colon G_1 \to G_2\) |
\(\varphi\) is a map from the vertices of \(G_1\) to the vertices of \(G_2\) (in this course, always an isomorphism) |
Notation 11.4.2 |
| \(G_1 \cong G_2\) |
\(G_1\) is isomorphic to \(G_2\) |
Notation 11.4.2 |
| \(P_n\) |
path of length \(n\) |
Notation 12.3.2 |
| \(C_n\) |
cycle of length \(n\) |
Notation 12.3.7 |
| \(\delta\) |
minimum valency |
Notation 13.2.5 |
| \(\Delta\) |
maximum valency |
Notation 13.2.5 |
| \(\delta(G)\) |
minimum valency of \(G\) |
Notation 13.2.5 |
| \(\Delta(G)\) |
maximum valency of \(G\) |
Notation 13.2.5 |
| \(\chi'(G)\) |
chromatic index of \(G\) |
Notation 14.1.4 |
| \(\chi'\) |
chromatic index |
Notation 14.1.4 |
| \(K_{m,n}\) |
complete bipartite graph |
Definition 14.1.12 |
| \(c(v)\) |
number of colours used on edges incident with \(v\) |
Notation 14.1.15 |
| \(R(n_1, \ldots, n_c)\) |
Ramsey number |
Theorem 14.2.8 |
| \(\chi(G)\) |
chromatic number of \(G\) |
Notation 14.3.4 |
| \(\chi\) |
chromatic number |
Notation 14.3.4 |
| \(F(G)\) |
set of faces of \(G\) |
Notation 15.1.7 |
| \(F\) |
set of faces |
Notation 15.1.7 |
| \(G^*\) |
planar dual of \(G\) |
Definition 15.1.8 |
| \(\hbox{MOLS}\) |
mutually orthogonal latin squares |
Definition 16.2.3 |
| \(a \equiv b \pmod{n}\) |
\(a\) is equivalent to \(b\) modulo \(n\) |
Notation 16.2.6 |
| \(\mathcal B\) |
collection of blocks in a design |
Definition 17.1.1 |
| \(v\) |
number of varieties in a design |
Notation 17.1.2 |
| \(b\) |
number of blocks in a design |
Notation 17.1.2 |
| \(r\) |
replication number (number of times each variety appears in the blocks) of a design |
Definition 17.1.3 |
| \(k\) |
cardinality of the blocks of a design |
Definition 17.1.3 |
| \(\lambda\) |
number of times each pair (or \(t\)-set) of varieties appear together in a block of a (\(t\)-)design |
Definition 17.1.3 |
| \((b,v,r,k,\lambda)\hbox{-design}\) |
BIBD with parameters \(b,v,r,k,\lambda\) |
Paragraph |
| \(\hbox{BIBD}\) |
balanced incomplete block design |
Definition 17.1.5 |
| \(\hbox{BIBD}(v,k,\lambda)\) |
BIBD with parameters \(v,k, \lambda\) |
Paragraph |
| \(\hbox{STS}(v)\) |
Steiner triple system on \(v\) varieties |
Notation 18.1.3 |