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Fill in the blanks below so that the resulting statement is true.

- If there is at least one edge connecting two vertices in a graph, the vertices are called _______.
- A sequence of such vertices and the edges connecting them is called _______.
- If this sequence of vertices and connecting edges begins and ends at the same vertex, it is called a _______.



Answer :

GinnyAnswer
Let's fill in the blanks to make the statements true step-by-step:

1. If there is at least one edge connecting two vertices in a graph, the vertices are called adjacent.

2. A sequence of such vertices and the edges connecting them is called a path.

3. If this sequence of vertices and connecting edges begins and ends at the same vertex, it is called a cycle.

Now, let's put it all together:

If there is at least one edge connecting two vertices in a graph, the vertices are called adjacent. A sequence of such vertices and the edges connecting them is called a path. If this sequence of vertices and connecting edges begins and ends at the same vertex, it is called a cycle.

These definitions are foundational in graph theory, which is a field of mathematics and computer science dealing with graphs, which are structures made up of vertices (or nodes) connected by edges.