In data structures, adjacent vertices play an important role in understanding the relationships between vertices in a graph. To put it simply, adjacent vertices are the vertices that are directly connected to a given vertex.

## Definition

Adjacent vertices are the vertices that share an edge with a particular vertex in a graph. In other words, if there is an edge connecting vertex A to vertex B, then A and B are considered adjacent to each other.

## Example

Let’s consider a simple example of a graph:

**Graph:**

In this example, the adjacent vertices for each vertex are as follows:

**A:** B (A-B)
**B:** A (A-B), C (B-C)
**C:** B (B-C), D (C-D)
**D:** C (C-D)

## Uses of Adjacent Vertices

The concept of adjacent vertices is widely used in various graph algorithms and applications. Some common uses include:

### Breadth-First Search (BFS)

In BFS, we visit all the adjacent vertices of a given vertex before moving on to the next level of vertices. This allows us to explore the graph in a breadth-first manner.

### Depth-First Search (DFS)

In DFS, we explore as far as possible along each branch before backtracking. The adjacent vertices help us determine the next vertex to visit during the traversal.

### Graph Coloring

Adjacent vertices play a role in graph coloring algorithms, where we assign colors to vertices such that no two adjacent vertices have the same color. By considering adjacent vertices, we can ensure that neighboring vertices have different colors.

## Conclusion

Understanding adjacent vertices is crucial for working with graphs and graph algorithms. They help us determine the relationships between vertices and enable us to perform various operations efficiently.

### 9 Related Question Answers Found

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Are you curious to know what exactly are nodes and edges in data structures? In this article, we will explore these fundamental concepts and understand their significance. So, let’s dive right in!