Refinements.

papers/bcr-2024-006-envelope-graph.md

@@ -13,9 +13,9 @@ Date: April 16, 2024
 
 ## Introduction
 
-[Graphs](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)) are mathematical structures that consist of a set of vertices (also known as nodes) and a set of edges connecting these vertices. Formally, a graph $G$ is represented as an ordered pair $(V, E)$, where $V$ is the set of vertices and $E$ is the set of edges. Each edge is a pair $\left\{ u, v \right\}$ (for undirected graphs) or an ordered pair $(u, v)$ (for directed graphs) representing a connection between vertices $u$ and $v$.
+[Graphs](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)) are mathematical structures that consist of a set of vertices (also known as nodes) and a set of edges connecting these vertices. Formally, a graph $G$ is represented as an ordered pair $`(V, E)`$, where $`V`$ is the set of vertices and $E$ is the set of edges. Each edge is a pair $`\left\{ u, v \right\}`$ (for undirected graphs) or an ordered pair $`(u, v)`$ (for directed graphs) representing a connection between vertices $`u`$ and $`v`$.
 
-The following example graph contains three vertices $V = \left\{ A, B, C \right\}$ and three directed edges $E = \left\{ (A, B), (B, C), (C, A) \right\}$ arranged in a "cycle":
+The following example graph contains three vertices $`V = \left\{ A, B, C \right\}`$ and three directed edges $`E = \left\{ (A, B), (B, C), (C, A) \right\}`$ arranged in a "cycle":
 
 ```mermaid
 graph LR