Okay, so I think if 2 vertices are adjacent to each other, they are incident to each other....or do I have it wrong? Is this just different terminology. I thought I was totally clear on this for my class, but now I am doubting myself reading the book and looking at my notes. I just want to know if I have it correct, and if I don't could someone explain to me what the difference is between the two. I found several wiki's and different university definitions, but none ever said that the two are alike and I'm confused and would like some reassurance. Thanks in advance.
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$\begingroup$Usually one speaks of adjacent vertices, but of incident edges.
Two vertices are called adjacent if they are connected by an edge.
Two edges are called incident, if they share a vertex.
Also, a vertex and an edge are called incident, if the vertex is one of the two vertices the edge connects.
$\endgroup$ 3 $\begingroup$If for two vertices $A$ and $B$ there is an edge $e$ joining them, we say that $A$ and $B$ are adjacent.
If two edges $e$ and $f$ have a common vertex $A$, the edges are called incident.
If the vertex $A$ is on edge $e$, the vertex $A$ is often said to be incident on $e$.
There is unfortunately some variation in usage. So you need to check the particular book or notes for the definition being used.
$\endgroup$ 1 $\begingroup$Excerpted from wikipedia:
Two edges of a graph are called adjacent (sometimes coincident) if they share a common vertex.
Similarly, two vertices are called adjacent if they share a common edge.
An edge and a vertex on that edge are called incident.
This terminology seems very sensible to my ear.
$\endgroup$ 1 $\begingroup$An edge "e" in a graph (Undirected or directed ) that is associated with the pair of vertices n and q is said to be incident on n and q, and n and q are said to be incident on e and to be adjacent vertices.
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