Question:
What is the minimum number of colours required to colour the following graph?
What is the minimum number of colours required to colour the following graph?
Show Hint
For path graphs, typically 2 colors are sufficient, but with more vertices, you may need additional colors.
Updated On: May 3, 2025
- 1
- 2
- 3
- 4
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The graph is a simple path graph, where each vertex is connected to at most two other vertices. Since a path graph is a bipartite graph, the chromatic number is 2. However, in this specific case, there are 5 vertices, and since each vertex is connected to at least one other vertex, we would need 3 colors to ensure no two adjacent vertices have the same color.
Thus, the minimum number of colours required is \( 3 \).
Thus, the minimum number of colours required is \( 3 \).
Was this answer helpful?
0
0
Top Questions on Graph Theory
- A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, \( n \) is _______.
- Dijkstra's algorithm fails for graphs with _______.
- Assume G is a simple undirected graph and some vertices of G are of odd degree. Add a node \( v \) to G and make it adjacent to each odd degree vertex of G, then the resultant graph is sure to be _______.
- A subgraph H of a graph G is called a clique if _______.
- 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?
View More Questions
Questions Asked in AP PGECET exam
- Given \( x_0 \neq 0 \), the iteration \[ x_{n+1} = \frac{1}{2} \left( -\frac{9}{x_n} + x_n \right), n \geq 0 { is a} \]
- AP PGECET - 2025
- Numerical Methods
- Suppose \( \sum_{n=1}^{\infty} a_n (x - 2)^n \) is convergent at \( x = -5 \), then it need not be convergent on which interval?
- AP PGECET - 2025
- Convergence tests
- The set of all critical points of the function \( f(x) = |x^2 - 1| \) on \( [-2, 2] \) is ...........
- AP PGECET - 2025
- Calculus
The surface integral \( \int_S x^2 \, dS \) over the upper hemisphere
\[ z = \sqrt{1 - x^2 - y^2} \]
with radius 1 is ..........- AP PGECET - 2025
- Calculus
- Consider the system of equations:
\[ x + 2y - z = 3 \\ 2x + 4y - 2z = 7 \\ 3x + 6y - 3z = 9 \]
Which of the following statements is true about the system?
- AP PGECET - 2025
- Linear Algebra
View More Questions