Adjacent vertices and Adjacent edges

Table of Contents

• Adjacent Vertices:
• Non-Adjacent Vertices:
  • Example1:
• Adjacent Edge:
• Non-Adjacent Edge:
  • Example2:

Adjacent Vertices:

Two vertices are said to be adjacent vertices if there is an edge between the two vertices.

Non-Adjacent Vertices:

Two vertices are said to be non-adjacent vertices if they do not have an edge between them.

Example1:

Let G= (V, E) be a graph where set of vertices V= {a, b, c, d} and set of edges E= {{a, b}, {a, c}, {b, d}}

• Vertex ‘a’ is adjacent to vertex ‘b’ because there is an edge between a and b.
• Vertex ‘a’ is adjacent to vertex ‘c’ because there is an edge between a and c.
• Vertex ‘b’ is adjacent to vertex ‘d’ because there is an edge between b and d.
• Vertex ‘a’ is non-adjacent to vertex ‘d’ because there is no edge between a and b.
• Vertex ‘c’ is adjacent to vertex ‘d’ because there is no edge between c and d.

Adjacent Edge:

Two edges in graph G are said to be adjacent edges if they share a common vertex.

Non-Adjacent Edge:

Two edges in graph G are said to be non-adjacent edges if they do not have a common vertex.

Example2:

• Edge e₁ and edge e₂ are adjacent edges because there is a common vertex ‘a’.
• Edge e₁ and edge e₃ are adjacent edges because there is a common vertex ‘b’.
• Edge e₂ and edge e₃ are non-adjacent edges because there is no common vertex between them.