Final version report practical 1

1 files changed, 3 insertions, 3 deletions

diff --git a/Practical1/report/notation.tex b/Practical1/report/notation.tex
index 07f9a34..6d01d9b 100644
--- a/Practical1/report/notation.tex
+++ b/Practical1/report/notation.tex
@@ -1,8 +1,8 @@
 \section{Notation}
 \label{sec:notation}
-I'm largely following Robson's notation \cite{robson}. For a graph $G=(V,E)$ and vertex $v\in V$, and edge $e\in E$, we write $d(v)$ for the degree of the vertex. $N(v)$ is the set of $v$'s neighbours, and $\iN(v)=N(v)\cup\{v\}$, $v$'s `inclusive neighbourhood'. Then $N^2(v)$ is the set of second order neighbours of $v$, excluding $v$: $N^2(v)=\{v_2 \in N(v_1) \mid v_1\in N(v)\} \setminus \{v\}$. If $\iN(v)\subseteq\iN(w)$, $v$ is said to dominate $w$, notation: $v>w$.
+I'm largely following Robson's notation \cite{robson}. For a graph $G=(V,E)$ and vertex $v\in V$, we write $d(v)$ for the degree of the vertex. $N(v)$ is the set of $v$'s neighbours, and $\iN(v)=N(v)\cup\{v\}$, $v$'s `inclusive neighbourhood'. Then $N^2(v)$ is the set of second order neighbours of $v$, excluding $v$: $N^2(v)=\{v_2 \in N(v_1) \mid v_1\in N(v)\} \setminus \{v\}$. If $\iN(v)\subseteq\iN(w)$, $v$ is said to dominate $w$, notation: $v>w$.
 
-We write `subgraph' for `vertex-induced subgraph', and $G\ex U$ for the subgraph induced on $G$ by $U$. For $v\in V$, we write $G\ex v$ for $G\ex\{v\}$. We use $e(v,w)$ for the predicate $(v,w)\in E$. We're strictly talking about non-directed graphs, so this is equivalent with $(w,v)\in E$.
+We write `subgraph' for `vertex-induced subgraph', and $G\ex U$ for the subgraph induced on $V\ex U$ by $G$. For $v\in V$, we write $G\ex v$ for $G\ex\{v\}$. We use $e(v,w)$ for the predicate $(v,w)\in E$. We're strictly talking about non-directed graphs, so this is equivalent with $(w,v)\in E$.
 
-Finally, We write `m.i.s.' for `maximum independent set' and $\ms(\cdots)$ for its size, the graph's independence number. The size of a graph or an m.i.s. is defined as the number of vertices and is written as $|G|$.
+Finally, We write `m.i.s.' for `maximum independent set' and $\ms(G)$ for its size in $G$, the graph's independence number. The size of a graph or an m.i.s. is defined as the number of its vertices and is written as $|G|$.