What is a multigraph?a.A graph with multiple componentsb.A graph with loops and parallel edgesc.A graph with no cyclesd.A graph with no vertices

Breakdown of the Problem

To identify what a multigraph is, let's evaluate the options provided and analyze their definitions.

Relevant Concepts

1. Graph: In graph theory, a graph consists of vertices (nodes) connected by edges (lines).
2. Multigraph: A multigraph is defined as a graph that may have multiple edges (parallel edges) connecting the same pair of vertices, as well as loops (edges that connect a vertex to itself).

Analysis and Detail

1. Option a (A graph with multiple components): This describes a disconnected graph but does not capture the essence of a multigraph, which specifically involves the edges.

2. Option b (A graph with loops and parallel edges): This accurately describes a multigraph. "Loops" and "parallel edges" are the key characteristics.

3. Option c (A graph with no cycles): This describes a specific type of graph known as a forest or tree, not a multigraph.

4. Option d (A graph with no vertices): This describes an empty graph, which is not related to the definition of a multigraph.

Verify and Summarize

From the analysis, option (b) is the only option that meets the criteria for a multigraph, as it allows both loops and multiple edges between the same vertex pairs.

Final Answer

The correct answer is b. A graph with loops and parallel edges.