# Connected but not adjacent vertex

Are there specific terms or adjectives in graph theory to name these two situations?

• Two vertices are non-adjacent (disjoint? I have seen that the term "disjoint" is rather used for paths with non-common vertices or edges).
• Two connected non-adjacent vertices (the shortest path or paths connecting them have a lenght $$> 1$$).
• For the first situation, I've only seen "non-adjacent", "nonadjacent", "non-neighbo[u]r[ing]". Larger groups of vertices, no pair of which are adjacent, are an "independent set" or "stable set". Some papers define "$u$ misses $v$" to mean $u$ is not adjacent to $v$. – j_random_hacker Aug 11 '19 at 15:01

You've exactly described the first situation, i.e. we indeed say that $$u$$ and $$v$$ are non-adjacent. For the second we do the same, but we want to also specify they are in the same component of $$G$$ which contains them if $$G$$ is not connected.