## Table of Contents

**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.

**Example**1:

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.

**Example**2:

- Edge e
_{1 }and edge e_{2 }are adjacent edges because there is a common vertex ‘a’. - Edge e
_{1 }and edge e_{3 }are adjacent edges because there is a common vertex ‘b’. - Edge e
_{2 }and edge e_{3 }are non-adjacent edges because there is no common vertex between them.

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