4. Which of the following is true?(a) A graph may contain no edge and many vertices(b) A graph may contain no edges and no vertices(c) A graph may contain no edges and no vertices(d) A graph may contain no vertices and many edges
Question
- Which of the following is true?(a) A graph may contain no edge and many vertices(b) A graph may contain no edges and no vertices(c) A graph may contain no edges and no vertices(d) A graph may contain no vertices and many edges
Solution
The correct answer is (a) A graph may contain no edge and many vertices.
This is because a graph in mathematics is a set of points, called vertices, and lines connecting those points, called edges. It is possible to have a graph with many vertices (points) but no edges (lines connecting the points).
Option (b) and (c) are the same and they state that a graph may contain no edges and no vertices. This is not possible because a graph, by definition, is a set of vertices. If there are no vertices, then it is not a graph.
Option (d) states that a graph may contain no vertices and many edges. This is also not possible because edges are lines that connect vertices. If there are no vertices, there can be no edges.
Similar Questions
Which of the following is true?Group of answer choicesA graph may contain many edges and no verticesA graph may contain no edges and many verticesA graph may contain no edges and no verticesA graph may contain no vertices and many edges
For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?
Which of the following statements for a simple graph is correct?(a) Every path is a trail(b) Every trail is a path(c) Every trail is a path as well as every path is a trail(d) Path and trail have no relation
For a given graph G having v vertices and e edges which is connected and has nocycles, which of the following statements is true?(a) v = e(b) v = e + 1(c) v + 1 = e(d) v = e – 1
Which of the following is true for a complete graph 𝐾𝑛K n ?A. It has 𝑛(𝑛−1)/2n(n−1)/2 edges.B. It has 𝑛n edges.C. It has 𝑛−1n−1 edges.D. It has 𝑛(𝑛+1)/2n(n+1)/2 edges.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.