Top MCQs on Graph Theory in Mathematics

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

Which of the following graphs is isomorphic to

Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and weight of the edge (vi, vj)  is ∣i–j∣. The weight of minimum spanning tree of G is ________.
 

The number of possible min-heaps containing each value from {1, 2, 3, 4, 5, 6, 7} exactly once is _______. Note -This was Numerical Type question.

Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is

Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?

Let G=(V,E) be a directed, weighted graph with weight function w:E→R. For some function f:V→R, for each edge (u,v)∈E, define w′(u,v) as w(u,v)+f(u)−f(v). Which one of the options completes the following sentence so that it is TRUE ? “The shortest paths in G under w are shortest paths under w′ too, _________”.

Which of the following statements is/are TRUE for undirected graphs? 

P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even. 

Consider the given graph Its Minimum Cost Spanning Tree is __________. (1) (2) (3) (4)