I am reading about graph theory.
A graph with $V$ vertices has at most $V(V-1)/2$ Edges
Proof: The total of $V^2$ possible pairs of vertices include $V$ self-loops and accounts twice for each edge between distinct vertices, so the number of edges is at most $(V^2 -V)/2 = V(V-1)/2$.
Question 1: Request your help in understanding above property with $V$ equal to $3$.
Isomorphic: Two graphs are isomorphic if we can change the vertex labels on one graph to make its set of edges identical to the other. It is challenging to solve isomorphic problem because there are $V!$ possible ways to label the vertices.
Question 2: Request your help on how the author came up with $V!$ possible ways.