The only translation I found is “sous-graphe induit”, but I don’t see anything linking on “vertex”. The only thing I see is that “vertex” means “sommet” when talking about graphs, which is a node.

Graph theory was a part of my studies so I can inform you for sure that you are looking for graphe (or sous-graphe depending on which one you want) induit.

The vertex is simply called un sommet.

The link between two vertices is called un arc.

Odds are most people will be unable to translate technical stuff. Even in the professional world people are encouraged to avoid using technical terms so the translation team doesn’t get muddled up.

Here is what I suggest:

1. Find the item on wikipedia (English)
2. Click Français on the left side bar
   https://en.wikipedia.org/wiki/Glossary_of_graph_theory#Subgraphs
   https://fr.wikipedia.org/wiki/Lexique_de_la_théorie_des_graphes
3. Search for the words you do know how to translate “sous-graphe” for example.

Best of luck with your French and maths.