Vertex

Description:

• End point

Adjacent vertices:

• Two vertices 𝑢 and 𝑣 in an undirected graph 𝐺 are called adjacent (or neighbors) in 𝐺 if 𝑢 and 𝑣 are endpoints of an edge 𝑒 of 𝐺.
• Such an edge 𝑒 is called incident with the vertices 𝑢 and 𝑣 and 𝑒 is said to connect 𝑢 and 𝑣.

Neighborhood, $N(v)$:

• The set of all neighbors of a vertex 𝑣 of 𝐺 = (𝑉, 𝐸), denoted by 𝑁(𝑣), is called the neighborhood of 𝑣.
• If 𝐴 is a subset of 𝑉, we denote by 𝑁(𝐴) the set of all vertices in 𝐺 that are adjacent to at least one vertex in 𝐴. So, $N(A)={\cup }_{v\in A}N(v)$

Degree of a vertex, $deg(v)$:

• The degree (or valency) of a vertex in an undirected graph is the number of edges incident with it
  • except that a loop at a vertex contributes twice to the degree of that vertex.
• Pendant: vertex with degree 1
• Isolate: degree o vertex